Recording multiple spatially-heterodyned direct to digital holograms in one digital image

ABSTRACT

Systems and methods are described for recording multiple spatially-heterodyned direct to digital holograms in one digital image. A method includes digitally recording, at a first reference beam-object beam angle, a first spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded first spatially-heterodyned hologram by shifting a first original origin of the recorded first spatially-heterodyned hologram to sit on top of a first spatial-heterodyne carrier frequency defined by the first reference beam-object beam angle; digitally recording, at a second reference beam-object beam angle, a second spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded second spatially-heterodyned hologram by shifting a second original origin of the recorded second spatially-heterodyned hologram to sit on top of a second spatial-heterodyne carrier frequency defined by the second reference beam-object beam angle; applying a first digital filter to cut off signals around the first original origin and define a first result; performing a first inverse Fourier transform on the first result; applying a second digital filter to cut off signals around the second original origin and define a second result; and performing a second inverse Fourier transform on the second result, wherein the first reference beam-object beam angle is not equal to the second reference beam-object beam angle and a single digital image includes both the first spatially-heterodyned hologram and the second spatially-heterodyned hologram.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of, and claims a benefit ofpriority under 35 U.S.C. 120 from copending utility patent applicationU.S. Ser. No. 10/421,444, filed Apr. 23, 2003, the entire contents ofwhich are hereby expressly incorporated herein by reference for allpurposes.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY-SPONSOREDRESEARCH OR DEVELOPMENT

This invention was made with United States Government support underprime contract No. DE-AC05-00OR22725 to UT-Battelle, L.L.C. awarded bythe Department of Energy. The Government has certain rights in thisinvention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to the field of direct-to-digitalinterferometry (spatial-heterodyne holography). More particularly, theinvention relates to methods and machinery for obtaining two-wavelengthdifferential-phase direct to digital interferograms(spatially-heterodyned holograms).

2. Discussion of the Related Art

The techniques and apparatus of basic direct to digital interferometry(holography) are well known to those of skill in the art.⁽¹⁻²⁾ Alimitation of this technology is the difficulty of tracking the phasechange in the object image when it involves multiple 2π steps. A 2πphase change occurs every time the optical object height changes by ½ ofthe laser wavelength. To obtain the full phase change of the objectimage, the multiple 2π's must be unwrapped. This unwrapping is oftenprone to errors, resulting in errors in the measured height of theobject. In addition, if the height changes more than 2π over a distanceless than the CCD pixel spacing at the object, the integral values of 2πof phase are completely lost (where 2π of phase shift occurs when theoptical object height changes by ½ wavelength of the imaging laser beamfor reflective imaging). To reduce the resulting errors, it is desirableto measure height variations at a much longer wavelength than that ofthe laser while still maintaining the lateral resolution of the shorterlaser wavelength. This goal is accomplished in other forms ofinterferometry and digital holography by separately acquiring the phasedata at two or more wavelengths and then looking at the difference ofthe phase measured by each wavelength.

The technique of using two wavelengths to measure large objects is wellknown in digital holography, holographic contouring and holographicinterferometry.⁽³⁾ In these techniques, phase information is obtainedindependently at two separate wavelengths. A digital hologram of anobject at a first wavelength is obtained, and then a second digitalhologram at a different wavelength is obtained. Each hologram isanalyzed to obtain their individual phase and amplitude information.Finally, these two sets of phase data are then processed to obtaindifference-phase data proportional to a scale length (i.e., the beatwavelength defined by the first wavelength and the second wavelength).Thus, the phase is measured at an effective wavelength much longer thaneither of the two probing wavelengths. In this way, height variationsmany times greater than the original laser wavelengths used have beenmeasured.

A serious limitation of this known approach is that noise in eachindividual image is uncorrelated to the noise in the other image. Whenthe difference between the two images is taken, the noise will not bereduced and is typically increased, thereby further reducing imagequality.

Heretofore, the requirement of tracking the phase change in the objectimage when it involves multiple 2π steps without reducing image qualityhas not been fully met. What is needed is a solution that addresses thisproblem.

SUMMARY OF THE INVENTION

There is a need for the following aspects of the invention. Of course,the invention is not limited to these aspects.

According to an aspect of the invention, a process of obtaining adifferential-phase hologram at a beat wavelength defined by a firstwavelength and a second wavelength includes: digitally recording a firstspatially-heterodyned hologram at the first wavelength, the firstspatially-heterodyned hologram including spatial heterodyne fringes forFourier analysis; and substantially simultaneously digitally recording asecond spatially-heterodyned hologram at the second wavelength that isdifferent from the first wavelength, the second spatially-heterodynedhologram including spatial heterodyne fringes for Fourier analysis; thenFourier analyzing the recorded first spatially-heterodyned hologram byshifting a first original origin of the recorded firstspatially-heterodyned hologram including spatial heterodyne fringes inFourier space to sit on top of a spatial-heterodyne carrier frequencydefined as a first angle between a first reference beam and a firstobject beam; Fourier analyzing the recorded second spatially-heterodynedhologram by shifting a second original origin of the recorded secondspatially-heterodyned hologram including spatial heterodyne fringes inFourier space to sit on top of a spatial-heterodyne carrier frequencydefined as a second angle between a second reference beam and a secondobject beam, the first angle and the second angle not substantiallyequal; applying a first digital filter to cut off signals around thefirst original origin and performing an inverse Fourier transform on theresult; applying a second digital filter to cut off signals around thesecond original origin and performing an inverse Fourier transform onthe result; and then determining a difference between a filteredanalyzed recorded first spatially-heterodyned hologram phase and afiltered analyzed recorded second spatially-heterodyned hologram phase.

According to another aspect of the invention, a machine to obtain adifferential-phase hologram at a beat wavelength defined by a firstwavelength and a second wavelength includes: a first source of coherentlight energy at a first wavelength; a second source of coherent lightenergy at a second wavelength coupled to the first source of coherentlight energy; a reference beam subassembly optically coupled to both thefirst source of coherent light and the second source of coherent light;an object beam subassembly optically coupled to the both the firstsource of coherent light and the second source of coherent light; and abeamsplitter optically coupled to both the reference beam subassemblyand the object beam subassembly, the beamsplitter directing a firstreference beam and a first object beam to generate a firstspatially-heterodyned hologram at a first spatial-heterodyne frequencyand directing a second reference beam and a second object beam togenerate a second spatially-heterodyned hologram at a secondspatial-heterodyne frequency that is different from the firstspatial-heterodyne frequency.

According to another aspect of the invention, a process of obtaining adifferential-phase hologram at a beat wavelength defined by a firstwavelength and a second wavelength includes: digitally recording a firstspatially-heterodyned hologram at the first wavelength, the firstspatially-heterodyned hologram including spatial heterodyne fringes forFourier analysis; Fourier analyzing the recorded firstspatially-heterodyned hologram by shifting a first original origin ofthe recorded first spatially-heterodyned hologram including spatialheterodyne fringes in Fourier space to sit on top of aspatial-heterodyne carrier frequency defined as a first angle between afirst reference beam and a first object beam; digitally recording asecond spatially-heterodyned hologram at the second wavelength that isdifferent from the first wavelength, the second spatially-heterodynedhologram including spatial heterodyne fringes for Fourier analysis;Fourier analyzing the recorded second spatially-heterodyned hologram byshifting a second original origin of the recorded secondspatially-heterodyned hologram including spatial heterodyne fringes inFourier space to sit on top of a spatial-heterodyne carrier frequencydefined as a second angle between a second reference beam and a secondobject beam; applying a first digital filter to cut off signals aroundthe first original origin and performing an inverse Fourier transform onthe result; applying a second digital filter to cut off signals aroundthe second original origin and performing an inverse Fourier transformon the result; and then determining a difference between a filteredanalyzed recorded first spatially-heterodyned hologram phase and afiltered analyzed recorded second spatially-heterodyned hologram phase.

According to another aspect of the invention, a process of obtaining adifferential-phase hologram at a beat wavelength defined by a firstwavelength and a second wavelength includes: digitally recording a firstspatially-heterodyned hologram at the first wavelength, the firstspatially-heterodyned hologram including spatial heterodyne fringes forFourier analysis; digitally recording a second spatially-heterodynedhologram at the second wavelength that is different from the firstwavelength, the second spatially-heterodyned hologram including spatialheterodyne fringes for Fourier analysis; Fourier analyzing the recordedfirst spatially-heterodyned hologram by shifting a first original originof the recorded first spatially-heterodyned hologram including spatialheterodyne fringes in Fourier space to sit on top of aspatial-heterodyne carrier frequency defined as a first angle between afirst reference beam and a first object beam; applying a first digitalfilter to cut off signals around the first original origin andperforming an inverse Fourier transform on the result; Fourier analyzingthe recorded second spatially-heterodyned hologram by shifting a secondoriginal origin of the recorded second spatially-heterodyned hologramincluding spatial heterodyne fringes in Fourier space to sit on top of aspatial-heterodyne carrier frequency defined as a second angle between asecond reference beam and a second object beam; applying a seconddigital filter to cut off signals around the second original origin andperforming an inverse Fourier transform on the result; and thendetermining a difference between a filtered analyzed recorded firstspatially heterodyne hologram phase and a filtered analyzed recordedsecond spatially-heterodyned hologram phase. Wherein digitally recordingthe first spatially-heterodyned hologram at the first wavelength iscompleted before digitally recording the second spatially-heterodynedhologram.

According to another aspect of the invention, a method of obtainingmultiple spatially-heterodyned holograms, comprises: digitallyrecording, at a first reference beam-object beam angle, a firstspatially-heterodyned hologram including spatial heterodyne fringes forFourier analysis; Fourier analyzing the recorded firstspatially-heterodyned hologram by shifting a first original origin ofthe recorded first spatially-heterodyned hologram to sit on top of afirst spatial-heterodyne carrier frequency defined by the firstreference beam-object beam angle; digitally recording, at a secondreference beam-object beam angle, a second spatially-heterodynedhologram including spatial heterodyne fringes for Fourier analysis;Fourier analyzing the recorded second spatially-heterodyned hologram byshifting a second original origin of the recorded secondspatially-heterodyned hologram to sit on top of a secondspatial-heterodyne carrier frequency defined by the second referencebeam-object beam angle; applying a first digital filter to cut offsignals around the first original origin and define a first result;performing a first inverse Fourier transform on the first result;applying a second digital filter to cut off signals around the secondoriginal origin and define a second result; and performing a secondinverse Fourier transform on the second result, wherein the firstreference beam-object beam angle is not equal to the second referencebeam-object beam angle and a single digital image includes both thefirst spatially-heterodyned hologram and the secondspatially-heterodyned hologram.

According to another aspect of the invention, an apparatus to obtainmultiple spatially-heterodyned holograms, comprises: a source ofcoherent light energy; a reference beam subassembly optically coupled tothe source of coherent light; an object beam subassembly opticallycoupled to the source of coherent light; a beamsplitter opticallycoupled to both the reference beam subassembly and the object beamsubassembly; and a single pixilated detection device coupled to thebeamsplitter that is used to digitally record both a firstspatially-heterodyned hologram at a first spatial-heterodyne frequencyand a second spatially-heterodyned hologram at a secondspatial-heterodyne frequency that is different from the firstspatial-heterodyne frequency, wherein both first spatially-heterodynedhologram and the second spatially-heterodyned hologram are generatedsubstantially at a focal plane of the single pixelated detection device.

According to another aspect of the invention, a method of obtainingmultiple spatially-heterodyned holograms, comprises: digitally recordinga first spatially-heterodyned hologram including spatial heterodynefringes for Fourier analysis; digitally recording a secondspatially-heterodyned hologram including spatial heterodyne fringes forFourier analysis; Fourier analyzing the recorded firstspatially-heterodyned hologram by shifting a first original origin ofthe recorded first spatially-heterodyned hologram including spatialheterodyne fringes in Fourier space to sit on top of aspatial-heterodyne carrier frequency defined as a first angle between afirst reference beam and a first object beam; applying a first digitalfilter to cut off signals around the first original origin andperforming an inverse Fourier transform on the result; Fourier analyzingthe recorded second spatially-heterodyned hologram by shifting a secondoriginal origin of the recorded second spatially-heterodyned hologramincluding spatial heterodyne fringes in Fourier space to sit on top of aspatial-heterodyne carrier frequency defined as a second angle between asecond reference beam and a second object beam; and applying a seconddigital filter to cut off signals around the second original origin andperforming an inverse Fourier transform on the result, wherein digitallyrecording the first spatially-heterodyned hologram is completed beforedigitally recording the second spatially-heterodyned hologram and asingle digital image includes both the first spatially-heterodynedhologram and the second spatially-heterodyned hologram.

According to another aspect of the invention, an apparatus to obtain aspatially-heterodyned hologram, comprises: a source of coherent lightenergy; a reference beam subassembly optically coupled to the source ofcoherent light; an object beam subassembly optically coupled to thesource of coherent light; a beamsplitter optically coupled to both thereference beam subassembly and the object beam subassembly; and apixelated detection device coupled to the beamsplitter, wherein thepixilated detection device is rotatable about an axis that issubstantially normal to a focal plane of the pixelated detection device.

These, and other, aspects of the invention will be better appreciatedand understood when considered in conjunction with the followingdescription and the accompanying drawings. It should be understood,however, that the following description, while indicating variousembodiments of the invention and numerous specific details thereof, isgiven by way of illustration and not of limitation. Many substitutions,modifications, additions and/or rearrangements may be made within thescope of the invention without departing from the spirit thereof, andthe invention includes all such substitutions, modifications, additionsand/or rearrangements.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings accompanying and forming part of this specification areincluded to depict certain aspects of the invention. A clearerconception of the invention, and of the components and operation ofsystems provided with the invention, will become more readily apparentby referring to the exemplary, and therefore nonlimiting, embodimentsillustrated in the drawings, wherein identical reference numeralsdesignate the same elements. The invention may be better understood byreference to one or more of these drawings in combination with thedescription presented herein. It should be noted that the featuresillustrated in the drawings are not necessarily drawn to scale.

FIG. 1 illustrates a schematic view of an optical layout for atwo-wavelength system, representing an embodiment of the invention.

FIG. 2 illustrates a conceptual representation of aspatially-heterodyning holographic system, representing an embodiment ofthe invention.

FIGS. 3A and 3B illustrate fringes produced by the reference and signalbeam of a square law device, representing an embodiment of theinvention.

FIGS. 4A and 4B illustrate the dependence of spatial frequency on theangle between the signal and reference beams, representing an embodimentof the invention.

FIG. 5A illustrates the magnitude response of a 2-D Fourier spectrum ofa phase-modulated sinusoidal signal, representing an embodiment of theinvention.

FIG. 5B illustrates the magnitude response result of moving the uppersideband to the center of the Fourier plane, representing an embodimentof the invention.

FIG. 5C illustrates filtered magnitude response results (the signal iscomplex and the phase of the spectrum encodes the surface profile),representing an embodiment of the invention.

FIG. 6 illustrates a conceptual representation of a two-wavelengthimaging system, representing an embodiment of the invention.

FIG. 7 illustrates a perspective view of an actual two-wavelength proofof principle system, representing an embodiment of the invention.

FIGS. 8A and 8B illustrate a two-wavelength spatially-heterodynedhologram and corresponding fast Fourier transform, respectively,representing an embodiment of the invention.

FIGS. 9A-9C illustrate two-wavelength direct-to-digital phase images ofa concave mirror, representing an embodiment of the invention.

FIG. 10A illustrates a 632.8 nm wavelength phase image of a 2.8 umresolution target, representing an embodiment of the invention.

FIG. 10B illustrates a 611.9 nm wavelength phase image of the 2.8 umresolution target, representing an embodiment of the invention.

FIG. 10C illustrates a 18.5 um beat wavelength phase image of the 2.8 umresolution target, representing an embodiment of the invention.

FIG. 11 illustrates a schematic view of another optical layout,representing an embodiment of the invention.

FIG. 12 illustrates a schematic view of another optical layout,representing an embodiment of the invention.

FIG. 13 illustrates a schematic view of another optical layout,representing an embodiment of the invention.

FIG. 14 illustrates a schematic view of another optical layout,representing an embodiment of the invention.

FIG. 15 illustrates a schematic view of another optical layout,representing an embodiment of the invention.

FIGS. 16A-16B illustrate a representation of the spatial-heterodynefringes of two SHHs a first (upper right to lower left) and a second(upper left to lower right) and their location in Fourier space,representing an embodiment of the invention.

FIG. 17 illustrates one possible orientation in Fourier space of threeSHHs acquired in one digital image, representing an embodiment of theinvention.

FIG. 18 illustrates a method of recording multiple spatially-heterodynedSHHs sequentially onto one digital image, where typically, the object ismoved between laser pulses; reference beam #1 is used for a first SHHand reference beam #2 is used for a second SHH; the reference beams havea different angle of incidence on the CCD so that they generate SHHswith different spatial-heterodyne frequencies, representing anembodiment of the invention.

FIG. 19 illustrates a method of recording multiple spatially-heterodynedSHHs of different objects or object surfaces simultaneously onto onedigital image; the total pathlength of Beam #1 from BS1 to the CCD isshorter than the total pathlength of Beam #2 from BS1 to the CCD by morethan the laser's coherence length; this results in the object andreference portions of Beam #1 being incoherent with respect to theobject and reference portions of Beam #2, representing an embodiment ofthe invention.

FIGS. 20A-20C illustrate a) a flipped first SHH; b) a second SHH; and c)a summed SHH, representing an embodiment of the invention.

FIGS. 21A-21C illustrate a) a Fourier transform of a flipped first SHH;b) a Fourier transform of a second SHH; c) a Fourier transform aftersummation of the flipped first SHH and the second SHH, representing anembodiment of the invention.

FIGS. 22A-22D show images of the magnitude and phase of two originalimages after reconstruction from a summed SHH, representing anembodiment of the invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

The invention and the various features and advantageous details thereofare explained more fully with reference to the nonlimiting embodimentsthat are illustrated in the accompanying drawings and detailed in thefollowing description. Descriptions of well known starting materials,processing techniques, components and equipment are omitted so as not tounnecessarily obscure the invention in detail. It should be understood,however, that the detailed description and the specific examples, whileindicating preferred embodiments of the invention, are given by way ofillustration only and not by way of limitation. Various substitutions,modifications, additions and/or rearrangements within the spirit and/orscope of the underlying inventive concept will become apparent to thoseskilled in the art from this disclosure.

Within this application several publications are referenced by Arabicnumerals, or principal author's name followed by year of publication,within parentheses or brackets. Full citations for these, and other,publications may be found at the end of the specification immediatelypreceding the claims after the section heading References. Thedisclosures of all these publications in their entireties are herebyexpressly incorporated by reference herein for the purpose of indicatingthe background of the invention and illustrating the state of the art.

The below-referenced U.S. Patent, and allowed U.S. Patent Application inwhich the issue fee has been paid, disclose embodiments that aresatisfactory for the purposes for which they are intended. The entirecontents of U.S. Pat. No. 6,078,392 issued Jun. 20, 2000, entitledDirect-To-Digital Holography, Holographic Interferometry, and Holovisionto Clarence E. Thomas, Larry R. Baylor, Gregory R. Hanson, David A.Rasmussen, Edgar Voelkl, James Castracane, Michele Sumkulet and LawrenceClow are hereby expressly incorporated by reference herein for allpurposes. The entire contents of allowed U.S. patent application Ser.No. 09/477,267 filed Jan. 4, 2000 (published PCT/US00/34982), entitledImprovements to Acquisition and Replay Systems for Direct-to-DigitalHolography and Holovision by Clarence E. Thomas and Gregory R. Hanson,in which the issue fee has been paid, are hereby expressly incorporatedby reference herein for all purposes.

The invention can include sequentially obtaining a spatially heterodyneddigital hologram of an object and then obtaining a second spatiallyheterodyned digital hologram at a slightly different wavelength. Eachspatially heterodyned digital hologram can then be analyzed to obtaintheir individual phase and amplitude (complex wave) information.Finally, the phase can be subtracted to obtain the difference-phaseproportional to the beat-wavelength. Of course, three or more spatiallyheterodyned digital holograms can be obtained in this way to define twoor more beat wavelengths, thereby enhancing the versatility of theapproach. Although this approach is a useful improvement, a limitationof this sequential approach is that noise in each individual image willtypically be uncorrelated to the noise in the other image. When thedifference between the two images is taken, the noise will not bereduced and may be increased, thereby reducing image quality.

The invention can include obtaining two spatially heterodyned digitalholograms (e.g., one each at two different wavelengths) substantiallysimultaneously using the same optics and CCD. This simultaneous approachis based on the two spatially heterodyned digital holograms occupyingdifferent spatial frequencies, preferably orthogonal spatial frequenciesor at least (quasi) substantially orthogonal spatial frequencies. Inthis way the two spatially heterodyned digital holograms can beseparated and processed in Fourier space during the analysis viaseparate digital filters. A direct to digital holographic system can besetup (deployed) such that two direct-to-digital interferograms(heterodyned holograms) can be acquired substantially simultaneously attwo separate wavelengths of the identical object (or substantiallysimilar area of the same object) on one CCD (charge coupled device) orother spatially pixelated detection device. The two separate wavelengthscan be generated by use of two separate lasers or one laser with abeamsplitter and a wavelength shifter.

Of course, the invention is not limited to the use of two spatiallyheterodyned holograms based on two wavelengths. Three or morewavelengths can be used to define two or more beat wavelengths.

This invention is based on the realization that two or more holograms atdifferent laser wavelengths can be recorded substantially simultaneouslyand then independently isolated in Fourier space by recording eachhologram at a different spatial carrier frequency. The spatial carrierfrequency is determined by the angle between the object beam andreference beam (which must be coherent) when they interfere on thesurface (e.g., focal plane) of the digital imaging device (e.g. CCD). Bysetting up the appropriate optical system, two or more object beams (atdifferent wavelengths) can be brought substantially simultaneously tothe CCD. At the same time, the two or more corresponding reference beams(one each for each object beam) can be brought to the CCD with theability to adjust the angles between the sets of object and referencebeams.

The two wavelengths can be generated with a single laser. For instancethe two wavelengths could be generated by switching the laser betweentwo different wavelengths in the sequential approach or by use of awavelength shifting device in the simultaneous approach.

It is important to appreciate that in the simultaneous (e.g., twowavelength) embodiment of the invention, system inherent artifacts (backreflections, vibrations etc) can be correlated (assuming the wavelengthdifference to be sufficiently small). This is important because uponsubtraction of the phase images (and/or amplitude images), systeminherent artifacts can be reduced (e.g., significantly) and theresulting image thereby improved, preferably substantially. This can bea very important commercial advantage of the invention.

Never before has a technique been shown for acquiring two holograms atdifferent wavelengths substantially simultaneously on one CCD. This typeof simultaneous acquisition is not possible without the use of thedirect to digital holographic technique involving spatial heterodyningof the object image (i.e., spatially-heterodyned holograms). Without theuse of spatial heterodyning, it is not possible to separate the twoholograms acquired substantially simultaneously on one CCD camera.Because the inventors use the interference of the object and referencebeams to generate precise linear fringes to spatially heterodyne theobject hologram, the inventors discovered that they can generate asecond spatially-heterodyned hologram at a different spatial frequencyby introducing a second optical beam into the optics system. As notedabove, the different spatial frequencies can be defined by focusing thetwo set of beams (object and reference) onto the focal (image) plane ofa CCD at two different angles. By generating the secondspatially-heterodyned hologram at a different spatial carrier frequency,the two images (of approximately the same object area) can be separatedand processed independently even though they are acquired in a singleCCD image. The invention can include combining or mixing of (e.g.,subtracting) the phase and/or object images from these two holograms totransform the scale length of the measured phase shift in each image tothe difference phase at the beat wavelength of the two images.

The invention can include measuring objects with spatial heightvariations much greater than the imaging laser wavelength over lateraldistances smaller than the wavelength.

The invention can include reduction of common-mode or correlated noise,such as back reflections and vibrations, by acquiring the twospatially-heterodyned digital holograms substantially simultaneously onthe same CCD and subtracting the resulting phase and/or amplitudeimages.

An alternative embodiment of the invention can include the mixing of thetwo 3-dimensional images in Fourier space rather than after transformingback to real space. This alternative embodiment can be implemented witha computationally intensive convolution in the frequency domain.

Two-Wavelength Imaging

The invention can include recording two holograms at two different laserwavelengths in one digital image (substantially simultaneously orsequentially). This invention (which can be termed: Dual wavelengthDirect to Digital Holography, 3DH) introduces a second wavelength toincrease the height range of the measurement. Two holograms at twodifferent laser wavelengths can be captured in single digital image byorienting the spatial-heterodyne fringes such that the two holograms areseparated in frequency space and can be reconstructed individually. AFourier transform of a single digital image can be performed, followedby digital filtering to separate, followed by individual reconstructionof the two holograms via an inverse Fourier transform. Once these twoholograms are reconstructed a phase subtraction can be used to determinethe phase response at a longer (or beat) wavelength determined by

$\lambda_{b} = \frac{\lambda\;\lambda_{2}}{\lambda - \lambda_{2}}$where λ and λ₂ are the two individual wavelengths. In this method, theobject under inspection is imaged by both wavelengths, which are setupto be collinear through the imaging optics. The reference beams for eachwavelength are brought together at the CCD separately so that the anglebetween their respective object waves can be independently controlledand set to obtain the desired spatial-heterodyne frequency. Insuring thetwo object waves are collinear guarantees that the phase images arealigned for calculating the beat phase image or difference phase image.However, it is important to note that the invention is not limited toembodiments where both wavelengths are collinear through the imagingoptics. It is only necessary that both wavelengths be collinear at theobject, the invention can include embodiments where both wavelengths arecollinear at the object but not other segments of the beam paths andsuch an embodiment is described in detail as example 5 below.Multiple-Wavelength Imaging

The invention can include recording three or more holograms of the sameobject in one digital image. This can include bringing three or morewavelengths into one imaging system and recording three or moreholograms, each with a different spatial frequency, in a single digitalimage. A limitation to recording more than two holograms in one digitalimage is the carryover of information between the spatially-heterodynedholograms (and the zero order image information) in Fourier space. Toprevent (minimize) this spreading or carryover of this informationbetween the holograms, the spatial-heterodyne frequencies areadvantageously adjusted to maximize (optimize) the separation betweenthe spatially-heterodyned holograms. Also, smaller radius digitalfilters may be required to prevent any carryover. Using smaller radiusfilters can have the affect of a reduction in the numerical aperture ofthe optical system. Alternatively, an aperture can be placed in theoptical system to reduce the spread in frequency space for eachindividual wavelength.

The recording of holograms of a single object surface at differentwavelengths allows the optimization of the beat wavelengths fordifferent surface heights. One may select three laser wavelengths sothat a short beat wavelength and a long beat wavelength are obtained.This can improve the flexibility and accuracy of the system.Alternatively, one or both lasers can have a tunable wavelength output.

The invention can include both methods and apparatus for acquiringmultiple holograms in a single high-speed digital image capture, andthen separating and isolating these holograms in Fourier space. Theinvention can also include a reconstruction algorithm for using twowavelengths to create a hologram representing a single longer beatwavelength.

As discussed above, Direct to Digital Holography (DDH) has beenpresented as a means for recording both phase and magnitude of a complexwavefront. As with any phase measurement technique, phase wraps occursuch that a phase difference of 360 degrees cannot be distinguished froma difference of 720 degrees. By using two individual wavelengths closeto one another, a long beat wavelength measurement can be made forimaging of much larger structures. The invention can include adual-wavelength direct to digital holography (3DH) system thatsubstantially simultaneously acquires DDH images at two differentwavelengths in a single image capture. These two images can then beprocessed to obtain a long beat wavelength hologram.

As also discussed above, because the inventors use the interference ofan object and a reference beam to spatially-heterodyne the object imageat a particular spatial frequency, the inventors can generate a secondspatially-heterodyned image at a different spatial frequency byintroducing a second laser beam at a slightly different wavelength intothe optics system. The second laser should be oriented with thenecessary angular differences to produce fringes that allow the twoimages (of the same object area) to be separated and processedindependently in frequency space (e.g., digital filtering) even thoughthey are acquired in a single digital image. The two differentwavelength lasers should have no (or very little) coherence between themto acquire both spatially-heterodyned images substantiallysimultaneously. A possible arrangement for such a two-wavelength systemis shown in FIG. 1. With this system, by calculating the phasedifference between the two reconstructed holograms, it is possible tomeasure surfaces with topographical (height) variations significantlygreater than the imaging laser wavelengths in a single digital image.These topographical features can include both step height changes(cliffs) and continuously sloped surfaces (spheres, wedges etc).

Referring to FIG. 1, the first laser 101 operating at a wavelength of λ₁is coupled to a fiber beamsplitter 102. An acousto-optic modulator (AOM)103 is coupled to the fiber beamsplitter 102. A fiber beamsplitter 104is coupled to acousto-optic modulator 103. A spatial filter 105 iscoupled to the fiber beam splitter 104. An illumination lens 106 isoptically coupled to the spatial filter 105. A beamsplitter 107 iscoupled to the illumination lens 106.

Still referring to FIG. 1, a multimode fiber 108 is also coupled to thefiber beamsplitter 102. An acousto-optic modulator 109 is coupled to themultimode fiber 108. A spatial filter 110 is coupled to theacousto-optic modulator 109. An illumination lens 111 is opticallycoupled to the spatial filter 110. A beamsplitter 112 is opticallycoupled to the illumination lens 111. A second laser 120 operating at awavelength of λ2 is coupled to a fiber beamsplitter 121. Anacousto-optic modulator 122 is coupled between the fiber beamsplitter121 and the fiber beamsplitter 104. A multimode fiber 123 is coupled tothe fiber beamsplitter 121. An acousto-optic modulator 124 is coupled tothe multimode fiber 123. A spatial filter 125 is coupled to theacousto-optic modulator 124. An illumination lens 126 is opticallycoupled to the spatial filter 125. A mirror 127 is optically coupledbetween the illumination lens 126 and the beamsplitter 112.

Still referring to FIG. 1, an imaging objective lens 130 is opticallycoupled between the beamsplitter 107 and an object 131 of interest. Arelay lens 132 is optically coupled between the beamsplitter 107 and abeamsplitter 140. A relay lens 133 is optically coupled between thebeamsplitter 112 and the beamsplitter 140. A CCD camera 150 is opticallycoupled to the beamsplitter 140. It can be appreciated that thisembodiment of the invention obviates the need for reference beammirrors. Through the use of the reference beam(s) subsystem that isconfigured through relay lens 133. It is an important aspect of theinvention that the spatially-heterodyned direct digital hologramsproduced by the object and reference beams at λ1, as well as the objectand reference beams operating at λ2 be focused on the focal (image)plane of the CCD Camera 150 at separate spatial frequencies, preferablyorthogonal spatial frequencies or at least quasi-(substantially)orthogonal spatial frequencies.

FIG. 1 shows a simplified configuration utilizing fiber optics and asimplified reference beam optics configuration. Each laser outputs intoa optical fiber. Each laser beam is then split into two beams to formthe object and reference beams by beamsplitters 102 and 121,respectively. Acousto-optic modulators (AOMs) are shown in these fiberpaths for shuttering the beams and adjusting individual power levels.The object beams are then combined into one optical fiber bybeamsplitter 104. This fiber then directs both object beams to theillumination lens which directs the object beams through thebeamsplitter 107 and the imaging objective lens onto the object. Thelight then reflects from the object, passes back through beamsplitter107 towards the relay lens. The reference beams, each in its own fiber,are directed through their individual illuminations lenses and ontobeamsplitter 112. Beamsplitter 112 combines the two reference beams intoone optical path. The positioning of the reference beams' optical fibersand illuminations lenses allows any angle desired to be created betweenthe two object beams. After passing through the relay lenses, the objectand reference beams are combined in beamsplitter 140 and then eachindividual wavelength object and reference beam pair interferes on theCCD. The desired spatial-heterodyne frequencies are then set byutilizing the reference beam fiber and illumination lens assemblies tocreate the required angle between each set of object beams andcorresponding reference beams at the CCD. In this drawing, spatialfilters are shown at the end of each fiber to insure good beam qualityin the imaging system. Using spatial filters at the ends of the opticalfibers would permit multimode fibers to be used.

Since the object and reference beams do not have identical opticalpaths, the wavefronts for each beam are not necessarily matched at theCCD. The matched wavefronts are important to generating the linearspatial-heterodyne fringes. The wavefronts can be sufficiently matchedsimply by choosing the appropriate lens for the reference beamillumination lens and adjusting the position of this lens.

The invention can include the use of two or more lasers operating at twoor more different frequencies. Alternatively, the invention can includethe use of one or more laser(s) coupled to one or more frequencyshifter(s) (e.g. one laser exciting two dye lasers via a beamsplitter)to provide two or more wavelengths. In addition, the invention caninclude the use of one or more laser(s) each having two or moreresonator ports, thereby reducing the number of beamsplitters requiredto provide a two-wavelength spatial-heterodyne configuration.

The two-wavelength spatial-heterodyne imaging technique is an extensionof the DDH technique that has been established in U.S. Pat. No.6,078,392 issued Jun. 20, 2000, entitled Direct-To-Digital Holography,Holographic Interferometry, and Holovision to Clarence E. Thomas, LarryR. Baylor, Gregory R. Hanson, David A. Rasmussen, Edgar Voelkl, JamesCastracane, Michele Sumkulet and Lawrence Clow and in U.S. patentapplication Ser. No. 09/477,267 filed Jan. 4, 2000 (publishedPCT/US00/34982), entitled Improvements to Acquisition and Replay Systemsfor Direct-to-Digital Holography and Holovision by Clarence E. Thomasand Gregory R. Hanson. In the case of DDH, we can represent a surfaceprofile as a signal in two spatial dimensions, z(x,y). For simplicityand without loss of generality, in our discussion below we will assumey=0 initially and simply deal with a one-dimensional signal. Thus, theprofile is simply z(x). We also omit some scaling constants that are dueto image magnification/demagnification.

In holography, a laser reflects from the surface and the height profileis captured in the phase of the laser wavefront. We can represent thisas

$\begin{matrix}{{s(x)} = {{a(x)}{\mathbb{e}}^{j\; 2\;\pi\frac{z{(x)}}{\lambda}}}} & (1)\end{matrix}$where a(x) is the amplitude of the reflection from the imaged surface,z(x) is the surface profile as a function of spatial position x, λ isthe wavelength of the light and j is Euler's Constant, or √{square rootover (−1)}. In traditional holography this signal is combined with areference beam whose incident angle is tilted relative to the signalbeam. This reference beam is coherent with the signal beam. We canrepresent this reference beam as

$\begin{matrix}{{r(x)} = {{b(x)}{\mathbb{e}}^{j\; 2\;\pi\frac{\theta_{0}x}{\lambda}}}} & (2)\end{matrix}$where θ₀ represents the reference beam angle relative to the signalbeam.

A conceptual representation of the holographic configuration is shown inFIG. 2. Referring to FIG. 2, an incident signal beam 210 is reflectedoff a surface 220 described by z(x). A signal beam 230, phase modulatedwith the surface profile, is collected along with a reference beam 240on a square-law device 250 such as a Photodetector or a Charge CoupledDevice (CCD) array.

Assuming perfect coherence between the two beams, the mathematicalequivalent is to multiply the signal by its complex conjugate. Thedetected signal is thus

${d(x)} = {\left( {{{a(x)}{\mathbb{e}}^{j\; 2\;\pi\frac{z{(x)}}{\lambda}}} + {{b(x)}{\mathbb{e}}^{j\; 2\;\pi\frac{\theta_{0}x}{\lambda}}}} \right)\left( {{{a^{*}(x)}{\mathbb{e}}^{{- j}\; 2\;\pi\frac{z{(x)}}{\lambda}}} + {{b^{*}(x)}{\mathbb{e}}^{{- j}\; 2\;\pi\frac{\theta_{0}x}{\lambda}}}} \right)}$

Applying Euler's Formula we obtain

$\begin{matrix}{{d(x)} = {{{a(x)}}^{2} + {{b(x)}}^{2} + {2{a(x)}{b(x)}{\cos\left( {{2\pi\;\frac{\theta_{0}x}{\lambda}} + {2\pi\;\frac{z(x)}{\lambda}}} \right)}}}} & (3)\end{matrix}$

This signal is a modulated sinusoid with a spatial frequency of

$\frac{\theta_{0}}{\lambda}$and a phase of

$\frac{z(x)}{\lambda}.$

An example of a two-dimensional signal of this type is shown in FIGS.3A-3B. FIG. 3B is an magnified portion of FIG. 3A. Referring to FIGS.3A-3B, the ‘fringes,’ or diagonal line patterns are sinusoidal intensitylevels produced by the reference and signal beam on the square lawdevice.

It should be noted that the spatial frequency is directly proportionalto the incident angle between the reference and object beams asillustrated in FIGS. 4A-4B. Referring to FIG. 4A an object beam 410 anda reference beam 420 are focused on a focal plane 430 of a CCD devicedefining an angle θ_(λ1). Referring to FIG. 4B the object beam 410 andthe reference beam 420 are focused on the focal plane 430 of the CCDdevice defining an angle θ_(λ2). It should be appreciated that the angleθ_(λ1) is less than the angle θ_(λ2) and, therefore the density of thefringes in FIG. 4B is higher. The density of the fringes is directlyproportional to the “spatial frequency”, or the angle between the signaland reference beams; the direction of the fringes depends on thelocation of the signal and reference beams.

In DDH, the signal represented by Eq. 3 is captured with a digitalcamera and transformed via Fast Fourier Transform algorithms to aspatial frequency representation.⁽⁴⁾ Using α to represent spatialfrequency, and

to represent convolution, the FFT produces

${D(\alpha)} = {{\left( {{a(x)}}^{2} \right)} + {\left( {{b(x)}}^{2} \right)} + {2{{A(\alpha)} \otimes {B(\alpha)} \otimes \left\{ {{\delta\left( {\alpha - \frac{\theta_{0}}{\lambda}} \right)} + {\delta\left( {\alpha + \frac{\theta_{0}}{\lambda}} \right)}} \right\} \otimes}\left( {\mathbb{e}}^{j\; 2\pi\frac{z{(x)}}{\lambda}} \right)}}$

In the frequency domain it is very easy to isolate the third term abovefrom the first two terms because the former is centered at the carrierfrequency represented by

$\frac{\theta_{0}}{\lambda}.$In DDH we take the signal centered at one sideband, shift the sidebandto the center of the frequency domain, and filter it with a filter w(x)as shown in the 2-D representation in FIG. 5.

FIGS. 5A-5C show: a) 2-D Fourier spectrum of phase-modulated sinusoidalsignal; b) result of moving the upper sideband to the center of theFourier plane; and c) filtered results. (Although these images show onlythe magnitude response, the signal in c) is complex and the phase of thespectrum encodes the surface profile.)

We take the signal of FIG. 5( c) and take the inverse FFT:

D ′ ⁡ ( α ) = W ⁡ ( α ) ⁢ { A ⁡ ( α ) ⊗ B ⁡ ( α ) ⊗ ⁢ ( ⅇ j ⁢ ⁢ 2 ⁢ π ⁢ z ⁡ ( x ) λ) } d ′ ⁡ ( x ) = - 1 ⁢ { D ′ ⁡ ( α ) } = w ⁡ ( x ) ⊗ { a ⁡ ( x ) ⁢ b ⁡ ( x ) ⁢ⅇ j ⁢ ⁢ 2 ⁢ π ⁢ z ⁡ ( x ) λ } ( 4 )

Applying Euler's Formula again we find

$\begin{matrix}{{d^{\prime}(x)} = {{w(x)} \otimes \left\{ {{a(x)}{b(x)}\left\{ {{\cos\left( {2\pi\frac{z(x)}{\lambda}} \right)} + {{jsin}\left( {2\pi\;\frac{z(x)}{\lambda}} \right)}} \right\}} \right\}}} & (5)\end{matrix}$

The real and imaginary components above are already available in ourdigital representation, so we can compute the surface profile at every xwith the formula

$\begin{matrix}{{z(x)} = {\frac{\lambda}{2\pi}{\tan^{- 1}\left( \frac{I}{R} \right)}}} & (6)\end{matrix}$where I and R are the real and imaginary components of the reconstructedimage. For 3DH utilizing two wavelengths, we perform the same operationsdescribed above a second time at a slightly different wavelength. Wewill discuss this second operation as if it occurs as a completelydifferent measurement, but the invention may perform the measurementssubstantially simultaneously to address, and preferably avoid, problemsof noise, processing speed, and imaging quality.

The operations for each of these two wavelengths are identical to theprevious single wavelength case, but with the different wavelength wecapture the opposite sideband or, alternately, digitally reverse thephase. In either case, after demodulation, the second signal is

d 2 ′ ⁡ ( x ) = - 1 ⁢ { D 2 ′ ⁡ ( α ) } = w ⁡ ( x ) ⊗ { a ⁡ ( x ) ⁢ b ⁡ ( x ) ⁢ⅇ - j2 ⁢ ⁢ π ⁢ z ⁡ ( x ) λ 2 } ( 7 )

We can combine these signals of Equations 4 and 7 digitally through amultiplicative process; focusing on the phase term, we find

$\begin{matrix}{{DualPhase} = {{{\mathbb{e}}^{{- j}\; 2\;\pi\frac{z{(x)}}{\lambda_{2}}}{\mathbb{e}}^{j\; 2\pi\frac{z{(x)}}{\lambda}}} = {\mathbb{e}}^{j\; 2\;\pi\;{z{(x)}}\frac{\lambda - \lambda_{2}}{{\lambda\lambda}_{2}}}}} & \left( {7a} \right)\end{matrix}$

We see that we have effectively performed holography with an opticaldevice of wavelength

$\begin{matrix}{\lambda_{b} = \frac{\lambda\;\lambda_{2}}{\lambda - \lambda_{2}}} & (8)\end{matrix}$

For instance, for a wavelength of 550 nm and 560 nm, the beat wavelengthλ_(b) is 30800 nm or 30.8 micrometers. Thus, a 2π phase wrap occursevery 15.4 micrometers instead of every 280 nm, allowing our system toimage much sharper, deeper depth transitions than is possible with asingle wavelength.

The dual phase equation (7a) can now be used to resolve the basic phaseambiguity in the computed low noise phase of either of the initialholograms. First, for z(x)>λ, equation (6) is written as:

$\begin{matrix}{{z(x)} = {\frac{\lambda_{1}}{2\pi}\left( {{\varphi_{1}(x)} \pm {2\pi\;{k_{1}(x)}}} \right)\mspace{31mu}{with}\mspace{14mu}{k_{1}(x)}\mspace{14mu}{an}\mspace{14mu}{integer}}} & (9)\end{matrix}$where φ₁(x)=tan⁻¹ (I/R) within the range of [−ππ]. Thus, based on themeasurement of φ₁(x), the value obtained for z(x) is ambiguous. From thedual phase, we obtain the surface profile

$\begin{matrix}{{z_{b}(x)} = {\frac{\lambda_{b}}{2\pi}\left( {{\varphi_{b}(x)} \pm {2\;\pi\;{k_{b}(x)}}} \right)}} & (10)\end{matrix}$where z_(b)(x) is the surface profile for the beat wavelength λ_(b).Note that z(x) and z_(b)(x) refer to the same surface profile. Since thebeat wavelength is much longer than the individual wavelengths, assumez_(b)(x)<λ_(b), then k_(b)(x)=0 and z_(b)(x) is unambiguously calculatedfrom equation (10). Therefore,

$\begin{matrix}{{z_{b}(x)} = {\frac{\lambda_{1}}{2\pi}\left( {{\varphi_{1}(x)} \pm {2\pi\;{k_{1}(x)}}} \right)}} & (11)\end{matrix}$

Rearranging, k₁(x) is calculated as

$\begin{matrix}{{k_{1}(x)} = {\frac{z_{b}(x)}{\lambda_{1}} - \frac{\varphi_{1}(x)}{2\pi}}} & (12)\end{matrix}$

The fact that k₁(x) must be an integer can reduce noise in the finalz(x) when computed using equation (9), if the noise in z_(b)(x) is lessthan λ₁/2. This is of great importance as it turns out experimentallythat by computing φ_(b)(x), not only is the directly interpretable rangefor z(x) expanded, but also its noise is amplified, in both cases byabout (λ/(λ−λ₂)).

It can, therefore, be appreciated that the invention can include thesteps of: digitally recording a first spatially-heterodyned hologram atthe first wavelength, the first spatially-heterodyned hologram includingspatial heterodyne fringes for Fourier analysis; Fourier analyzing therecorded first spatially-heterodyned hologram by shifting an origin ofthe recorded first spatially-heterodyned hologram including spatialheterodyne fringes in Fourier space to sit on top of aspatial-heterodyne carrier frequency defined as a first angle between afirst reference beam and a first object beam; digitally recording asecond spatially-heterodyned hologram at the second wavelength that isdifferent from the first wavelength, the second spatially-heterodynedhologram including spatial heterodyne fringes for Fourier analysis;Fourier analyzing the recorded second spatially-heterodyned hologram byshifting an origin of the recorded second spatially-heterodyned hologramincluding spatial heterodyne fringes in Fourier space to sit on top of aspatial-heterodyne carrier frequency defined as a second angle between asecond reference beam and a second object beam; applying a first digitalfilter to cut off signals around a first original origin and performingan inverse Fourier transform on the result; applying a second digitalfilter to cut off signals around a second original origin and performingan inverse Fourier transform on the result; and then determining adifference between a filtered analyzed recorded firstspatially-heterodyned hologram phase and a filtered analyzed recordedsecond spatially-heterodyned hologram phase. While determining thedifference requires that the other steps be completed first, theinvention is not limited to a particular sequence of the other steps,other than the individual meta-subsequences of recording, followed byanalysis, followed by filtering.

Mathematically there are several approaches for calculating the phasedifference between two complex images. In a first approach, a complexdivision can be performed that results and a complex images having amagnitude equal to the ratio of the two image intensities and a phaseequal to the difference between the two image phases. In a secondapproach, multiplying the complex conjugate of one complex image by theother results in a complex image with intensity equal to themultiplication of the two image intensities and phase equal to thedifference between the two image phases. Incidentally, the secondapproach is interesting in that the complex conjugate can be obtainedwith no extra calculation by simply choosing the complex conjugatesideband in frequency space during reconstruction. A third approach caninclude subtracting the two phase images, but wraps in the phase imagesmust be dealt with by implementing (writing and/or coding) a phase awaresubtraction. Of course, the invention is not limited to theseapproaches. Generically, the approaches can be described as determininga difference between first and second reconstructed hologram phases. Theinvention can capture images for both wavelengths with a single imagecapture operation by setting up quasi-orthogonal fringes, as illustratedin FIG. 6. Two sets of fringes are seen in the portion of the image inFIG. 6 on the left, with lines running from the lower left to the upperright representing one wavelength and lines running from the upper leftto the lower right representing the other wavelengths. These are Fouriertransformed together to produce two independent sets of sidebands.Sidebands from the first set of fringes (blue) are in the upper left andlower right of the portion of the image in FIG. 6 on the right.Sidebands from the second set of fringes are in the lower left and upperright of the portion of the image in FIG. 6 on the right. The sidebandsin the dashed circles are used to produce the phase difference signal atthe effective longer wavelength. This allows two images to be isolatedin frequency space and eliminates problems associated with acquiringimages at different points in time.

A tabletop proof of principle (POP) system for the two-wavelength 3DHconcept has been implemented and is shown in FIG. 7. The POP system hasbeen used to verify the two-wavelength imaging capabilities and identifytechnical challenges for making a robust 3DH system for metrology andinspection. A beat wavelength of 18.527 um is obtained with the POPsystem using laser wavelengths of 632.8 nm and 611.9 nm. FIG. 8 shows ahologram taken with the POP system showing the two sets of fringes in acheckerboard pattern along with the corresponding FFT showing theisolated sidebands created by the two fringe patterns.

FIGS. 9 and 10 give two examples of phase imagery from the POP system.FIG. 9 shows phase information from a concave mirror with a 52.8 mmradius of curvature. The left and center images show the phaseinformation obtained by the two individual wavelengths while the rightshows the beat wavelength image. This example quickly demonstrates theadvantage of the beat wavelength. For this mirror surface, only one wrapappears in the beat wavelength image while over 30 wraps occur in theindividual wavelength images. The shape of the mirror surface could alsobe determined by unwrapping the individual wavelength images; however,phase unwrapping is a complicated problem that is greatly affected bynoise in the image.

FIG. 10 is a phase image of a gold on gold resolution target with aheight of 2.8 microns. The two left most images are phasereconstructions for the two individual wavelengths. These individualwavelengths have wrapped 9 times plus a fraction of a wrap. The heightobtained by the single wavelengths is a measure of the remainingfraction after wrapping. Thus, the 632.8 nm wavelength image looks as ifthe structure is only 17 nm high and the 612 nm wavelength imagemeasures the structure to be 102 nm high. The rightmost image is thetwo-wavelength phase reconstruction. With a beat wavelength of 18.5 umno wraps occur and the true height measurement is calculated from thephase height difference. The phase/height differences between the twolevels in the third image are 111 degrees/2.865 um as expected.

The POP system verifies the extensibility of the DDH system to largerobjects with two wavelengths captured in a single image by the 3DHtechnique. Three key issues became apparent while using the POP system.1.) Previously we had only imaged fairly flat objects with respect tothe individual wavelengths. When imaging objects with large slopes, thecarrier is spread out in frequency space. This will require more robustsearch routines to find and isolate the information encoded by the twoindividual wavelengths. 2.) Phase noise in the beat wavelength image(normalized to wavelength) is approximately equal to that in theindividual wavelength images; however, a single degree of phase noise inthe beat wavelength image corresponds to a height error 30 times greaterthan the same phase noise in a single wavelength image. 3.) In the POPsystem, illumination is impinged on the sample at a fairly large angleto reduce back reflections in the optics. Based on experimentalexperience with actual; samples, on-axis illumination is preferred ifthe back reflection noise can be reduced. On-axis illumination allowsthe steepest slopes in all directions to be present and still beproperly imaged.

EXAMPLES

Specific embodiments of the invention will now be further described bythe following, nonlimiting examples which will serve to illustrate insome detail various features. The following examples are included tofacilitate an understanding of ways in which the invention may bepracticed. It should be appreciated that the examples which followrepresent embodiments discovered to function well in the practice of theinvention, and thus can be considered to constitute preferred modes forthe practice of the invention. However, it should be appreciated thatmany changes can be made in the exemplary embodiments which aredisclosed while still obtaining like or similar result without departingfrom the spirit and scope of the invention. Accordingly, the examplesshould not be construed as limiting the scope of the invention.

Example 1

Referring to FIG. 11, a free space exemplary embodiment of the inventionis depicted using reference mirrors. A first laser 1101 operating at awavelength A, is optically coupled to a beamsplitter 1103. Abeamsplitter 1105 is optically coupled to the beamsplitter 1103. Anillumination lens 1107 is optically coupled to the beamsplitter 1105. Abeamsplitter 1109 is optically coupled to the illumination lens 1107. Animaging lens 1110 is optically coupled to the beamsplitter 1109. An areaof a surface of an object 1112 of interest is optically coupled to theimaging lens 1110. An illumination lens 1111 is optically coupled to thebeamsplitter 1103. A beamsplitter 1113 is optically coupled to theillumination lens 1111. An imaging lens 1115 is optically coupled to thebeamsplitter 1113. A reference mirror 1117 is optically coupled to theimaging lens 1115. A beamsplitter 1119 is optically coupled thebeamsplitter 1113.

Still referring to FIG. 11, a second laser 1121 operating at awavelength λ₂ is optically coupled to a beamsplitter 1123. A mirror 1125is optically coupled to the beam splitter 1123. A mirror 1127 isoptically coupled to the mirror 1125 and the beamsplitter 1105. A mirror1129 is optically coupled to the beamsplitter 1123. A mirror 1131 isoptically coupled to the mirror 1129. An illumination lens 1133 isoptically coupled to the mirror 1131. A beamsplitter 1135 is opticallycoupled to the illumination lens 1133 and to the beamsplitter 1119. Animaging lens 1137 is optically coupled to the beamsplitter 1135. Areference mirror 1139 is optically coupled to the imaging lens 1137. Abeamsplitter 1140 is optically coupled to the beamsplitter 1109 and tothe beamsplitter 1119. A charge coupled device camera 1150 is opticallycoupled to the beam splitter 1140. FIG. 11 shows one basicimplementation in which the object and reference beams utilize identicaloptical components to insure matched wavefronts between the object beamand the reference beam for each wavelength. Each laser output is dividedinto two beams by the first beamsplitters encountered (BS1 and BS2,respectively, for λ₁ and λ₂) These two beams then become the object andreference beams for that laser wavelength. The object beams for bothwavelengths are then brought together in one optical path bybeamsplitter BS3. The two object beams are then directed to the imaginglens by beamsplitter BS4. The reflected object image is then directedback towards the CCD by passing through BS4. The reference beams aredirected towards their respective reference lenses and mirrors bybeamsplitters BS5 and BS6. Upon reflection from the reference mirrors,each of the reference beams passes back through its beamsplitter, BS5and BS6. Beamsplitter BS7 then is used to combine the two referencebeams into one optical path but with a small angular difference betweenthem, created by the positioning of BS7. The final beamsplitter BS8combines the collinear object beams with the reference beams so thatthey then interfere on the CCD. Since λ₁ and λ₂ are not coherent withrespect to one another, two separate spatially heterodyned holograms arecreated with different spatial frequencies. The spatial frequencies areset by the angle between the object and reference beams for eachwavelength. These angles are set by and adjusted by the positioning ofBS7 and BS8.

Example 2

Referring to FIG. 12, a free space exemplary embodiment of the inventionis depicted where reference mirrors are omitted. A helium neon laser1201 operating at a wavelength of 611.9 nanometers is optically coupledto a variable attenuator 1203. A variable beamsplitter 1205 is opticallycoupled to the variable attenuator 1203. A spatial filter 1207 isoptically coupled to the variable beamsplitter 1205. A collimating lens1209 is optically coupled to the spatial filter 1207. A beamsplitter1211 is optically coupled to the collimating lens 1209. An illuminationlens 1213 is optically coupled to the beamsplitter 1211. A beamsplitter1215 is optically coupled to the illumination lens 1213. An objectivelens 1217 is optically coupled to the beamsplitter 1215. A target 1219having a surface area of interest is optically coupled to the objectivelens 1217. A tube lens 1220 is optically coupled to the beamsplitter1215. A spatial filter 1221 is optically coupled to the variablebeamsplitter 1205. A collimating lens 1223 is optically coupled to thespatial filter 1221. A mirror 1225 is optically coupled to thecollimating lens 1223. A mirror 1227 is optically coupled to the mirror1225. A mirror 1229 is optically coupled to the mirror 1227. A referencelens 1231 is optically coupled to the mirror 1229. A mirror 1233 isoptically coupled to the reference lens 1231. A mirror 1235 is opticallycoupled to the mirror 1233. A beamsplitter 1237 is optically coupled tothe mirror 1235. A tube lens 1239 is optically coupled to thebeamsplitter 1237. A beamsplitter 1241 is optically coupled to the tubelens 1239 and to the tube lens 1220. A charge coupled device camera 1243is optically coupled to the beamsplitter 1241.

Still referring to FIG. 12, a second helium neon laser 1251 operating ata wavelength of 632.8 nanometers is optically coupled to a mirror 1253.A variable attenuator 1255 is optically coupled to the mirror 1253. Avariable beamsplitter 1257 is optically coupled to the variableattenuator 1255. A spatial filter 1259 is optically coupled to thevariable beamsplitter 1257. A collimating lens 1261 is optically coupledto the spatial filter 1259. A mirror 1263 is optically coupled to thecollimating lens 1261 and to the beamsplitter 1211. A mirror 1265 isoptically coupled to the variable beamsplitter 1257. A spatial filter1267 is optically coupled to the mirror 1265. A collimating lens 1269 isoptically coupled to the spatial filter 1267. A reference lens 1271 isoptically coupled to the collimating lens 1269. A mirror 1273 isoptically coupled to the reference lens 1271 and to the beamsplitter1237.

FIG. 12 shows a schematic of the proof-of-principle system used todemonstrate the first two-wavelength spatial-heterodyne imaging. A 632.8nm HeNe laser and a 611.9 nm HeNe laser are used to generate the twodifferent wavelengths. These wavelengths have a beat wavelength of 18.5μm. Each laser beam passes through a variable attenuator and then avariable beamsplitter. The variable beamsplitters generates two outputbeams with an infinitely variable power balance between the two outputbeams. The variable attenuators are then used to set the total beampower. Spatial filters located after the variable attenuators filter thebeams to insure a clean Gaussian beam structure. Collimating lenses areused to collect the light from the spatial filters. The object beams arethen combined by a beamsplitter, BS1, so that they are collinear. Theythen path through the illumination lens, which focuses the beams intothe objective lens. These beams then reflect off of the object surfaceand pass back through the objective lens. Beamsplitter BS2 then reflectsthese object beams towards the tube lens and beamsplitter BS4 which willcombine the object and reference beams.

The reference beams also pass through spatial filters and collimatinglens. Mirrors may be used to adjust pathlengths and correctly positionthe beams. The beams then pass through the reference beam illuminationlenses which give the beams the correct wavefront shape for matching tothe object beam wavefronts. Additional mirrors are used to bring the tworeference beams together at beamsplitter BS3. The two reference beamsthen pass through the tube lens and onto the beamsplitter BS4. Theobject and reference beams are then combined into one path by BS4 sothat they interfere at the CCD, creating two separate interferencepatterns, one for each wavelength. The interference fringes are set tobe approximately orthogonal by adjusting the angle of interferencebetween the individual wavelength object and reference beams byadjusting BS3 for the 632.8 nm wavelength, and mirror M1 for the 611.9nm wavelength.

Example 3

Referring to FIG. 13, an exemplary embodiment of the invention isdepicted that uses optical fibers and reference mirrors. A laser 1301operating at a wavelength of λ₁ is optically coupled to a beamsplitter1303. An optical fiber 1304 is coupled to the beamsplitter 1303. Abeamsplitter 1305 is coupled to the fiber 1304. A fiber 1306 is coupledto the beamsplitter 1305. An illumination lens 1307 is optically coupledto the fiber 1306. A beamsplitter 1309 is optically coupled to theillumination lens 1307. An imaging lens 1311 is optically coupled to thebeamsplitter 1309. A object 1313 having an area of interest is opticallycoupled to the imaging lens 1311. An optical fiber 1315 is coupled tothe beamsplitter 1303. An illumination lens 1317 is optically coupled tothe fiber 1315. A beamsplitter 1319 is optically coupled to theillumination lens 1317. An imaging lens 1321 is optically coupled to thebeamsplitter 1319. A reference mirror 1323 is optically coupled to theimaging lens 1321.

Still referring to FIG. 13, another laser 1327 operating at a wavelengthof λ₂ is optically coupled to a beamsplitter 1329. An optical fiber 1330is coupled to the beamsplitter 1329. An optical fiber 1330 is coupled tothe beamsplitter 1329 and to the beamsplitter 1305. An optical fiber1331 is coupled to the beamsplitter 1329. An illumination lens 1333 isoptically coupled to the fiber 1331. A beamsplitter 1335 is opticallycoupled to the illumination lens 1333 and to the beamsplitter 1325. Animaging lens 1337 is optically coupled to the beamsplitter 1335. Abeamsplitter 1340 is optically coupled to the beamsplitter 1325 and tothe beamsplitter 1309. A charge coupled device camera 1350 is opticallycoupled to the beamsplitter 1340.

FIG. 13 shows one preferred optical setup for acquiring the twoholograms substantially simultaneously. In this configuration, one oftwo interposed meta-subassemblies includes λ₁ from Laser #1 is shown inthe configuration described in U.S. patent application Ser. No.09/477,267 filed Jan. 4, 2000 (published PCT/US00/34982), entitledImprovements to Acquisition and Replay Systems for Direct-to-DigitalHolography and Holovision by Clarence E. Thomas and Gregory R. Hanson Tofirst meta-subassembly is combined with a second meta-subassembly thatincludes λ₂ from Laser #2. In the object arm of this combined system,both wavelengths are collinear through the fiber and optical system. Inthe reference arm, we produce two separate reference beams (one for eachwavelength). The λ₁ reference arm is in the standard configuration,while the λ₂ reference arm is rotated 90 degrees so that it may becombined with the λ₁ reference beam via a beamsplitter. Thisbeamsplitter allows the λ₂ reference beam to be adjusted to produce thedesired spatial fringes on the CCD independent of the λ₁ spatial fringesproduced with the standard beamsplitter located just in front of the CCDcamera. The λ₂ reference beam is angle of incidence is adjusted toproduce the fringes on the CCD at an angle approximately perpendicularto the λ₁ fringes. Although having the two sets of fringes approximatelyperpendicular is the preferred implementation, it is not a requirement.

The CCD image is acquired and transformed to frequency space via a FFToperation. In frequency space, we now have two spatially-heterodynedimages of the same object but acquired at two different wavelengths. Noweach spatially-heterodyned image can be isolated from the other imageand from the zero order reference beam, and then transformed back toreal space to yield the phase and amplitude image. Once this is done toboth spatially-heterodyned images, their phase (and amplitude ifdesired) difference can be obtained simply by subtracting the phasevalues. The beat wavelength produced by this subtraction is then givenby λ_(b)=λ₁*λ₂/(λ₁−λ₂)

Example 4

Referring to FIG. 14, a exemplary embodiment of the invention utilizesoptical fiber for some connections and omits the use of referencemirrors is depicted. A laser 1401 operating at a wavelength of λ₁ isoptically coupled to a beamsplitter 1403. A optical fiber 1405 iscoupled to the beamsplitter 1403. A beamsplitter 1407 is coupled to theoptical fiber 1405. An optical fiber 1409 is coupled to the beamsplitter1407. An illumination lens is 1411 is optically coupled to the fiber1409. A beamsplitter 1413 is optically coupled the illumination lens1411. An imaging lens 1415 is optically coupled to the beamsplitter1413. An object 1417 having a surface area of interest is opticallycoupled to the imaging lens 1415. An optical fiber 1419 is coupled tothe beamsplitter 1403. An illumination lens 1421 is optically coupled tothe fiber 1419.

Still referring to FIG. 14, a laser 1423 operating at a wavelength of λ₂is optically coupled to a beamsplitter 1425. An optical fiber 1427 iscoupled to the beamsplitter 1425 and to the beamsplitter 1407. Anoptical fiber 1429 is coupled to the beamsplitter 1425 and to theillumination lens 1421. A beamsplitter 1430 is optically coupled to theillumination lens 1421 and to the beamsplitter 1413. A charge coupleddevice camera 1440 is optically coupled to the beamsplitter 1430.

Another preferred optical configuration is shown in FIG. 14. In thisconfiguration, the reference beam paths which were carefully matched tothe object beam path are replaced with a lens or lens system. This lensor lens system produces the required wavefront to produce the requiredlinear fringes when mixed with the object beam of the same wavelength.This technique of replacing the reference beam path with a simple lenssystem is a common practice in digital holography, holographiccontouring and holographic interferometry. However, the inclusion of twowavelengths into one system to produce two separate hologramssubstantially simultaneously on one CCD camera is novel. In ourconfiguration, the object arm is unchanged from the previous layout(both wavelengths brought together into one fiber) but the referencearms are completely removed. In their place is a lens or lens systemwhich will collect the light from the fiber output and focus it onto theCCD with the required wavefront curvature to match the object beam. Thesecond wavelength reference beam is brought into the beamsplitter at anangle relative to the first. The position and angle of this second beamis adjusted to produce the desired orientation of the linear fringes,i.e. rotated approximately 90 degrees to the first set of fringes. Theprocessing of the CCD image then proceeds as previously discussed.

Example 5

Referring to FIG. 15, another exemplary embodiment of the invention thatutilizes optical fiber for some connections and omits the use ofreference mirrors is depicted. This embodiment uses two CCD cameras tohelp maintain lateral resolution. A laser 1501 operating at a wavelengthof λ₁ is optically coupled to a beamsplitter 1503. A optical fiber 1505is coupled to the beamsplitter 1503. A beamsplitter 1507 is coupled tothe optical fiber 1505. An optical fiber 1509 is coupled to thebeamsplitter 1507. An illumination lens is 1511 is optically coupled tothe fiber 1509. A beamsplitter 1513 is optically coupled theillumination lens 1511. An imaging lens 1515 is optically coupled to thebeamsplitter 1513. An object 1517 having a surface area of interest isoptically coupled to the imaging lens 1515. An optical fiber 1519 iscoupled to the beamsplitter 1503. An illumination lens 1523 is opticallycoupled to the fiber 1519.

Still referring to FIG. 15, a laser 1523 operating at a wavelength of λ₂is optically coupled to a beamsplitter 1525. An optical fiber 1527 iscoupled to the beamsplitter 1525 and to the beamsplitter 1507. Anoptical fiber 1529 is coupled to the beamsplitter 1525. An illuminationlens 1521 is optically coupled to the optical fiber 1529. A beamsplitter1550 is optically coupled to the beamsplitter 1513. A first etalon 1555is optically coupled to the beamsplitter 1550. A beamsplitter 1530 isoptically coupled to the first etalon 1555 and the illumination lens1521. A first charge coupled device camera 1540 is optically coupled tothe beamsplitter 1530. A second etalon 1560 is also optically coupled tothe beamsplitter 1550. A mirror 1565 is optically coupled to the secondetalon 1560. A beamsplitter 1570 is optically coupled to the secondetalon 1560 and the illumination lens 1523. A second charge coupleddevice camera 1575 is optically coupled to the beamsplitter 1570.

Still referring to FIG. 15, the first etalon 1555 passes λ₂ and thesecond etalon 1560 passes λ₁. It is important that the beam path lengthsfor the two wavelengths (λ₁ from object 1517 to the first CCD camera1540 and λ₂ from object 1517 to the second CCD camera 1575) be adjustedso that the magnification between the object and each camera issubstantially identical for both wavelengths. In this way, lateralresolution can be substantially maintained.

Example 6

Another embodiment of the invention can include a method for recordingmultiple spatially-heterodyned direct to digital SHHs in one digitalimage. This embodiment of the invention encompasses the recording of twoor more complex wavefronts (or holograms), simultaneously (orsequentially but in one digital image), by utilizing differentspatial-heterodyne frequencies so that in Fourier space the individualcomplex wavefronts are located at different spatial frequenciespermitting each to be isolated, filtered, and inverse Fouriertransformed.

A limitation the ORNL patented Direct-To-Digital (DDH) technology is thesignificant time required to acquire each spatially-heterodyned hologram(SHH) and then Fourier Transform (FT) the digital image containing theSHH. SHH's can be generated much faster than digital cameras can readthem out. If two or more SHH's can be recorded in 1 digital image, theoverall acquisition speed of the system can be increased. Thecomputational time required to FT a SHH image can be up to 50% of thetotal analysis time, thus the ability to process two or more SHH's inone FT can result in a significant savings in computation time.

A key to this exemplary embodiment of the invention is the realizationthat two or more spatially-heterodyned holograms (SHHs) can be recordedsimultaneously and then independently isolated in Fourier space byrecording each SHH at a different spatial-heterodyne frequency. Thespatial-heterodyne frequency is determined by the angle between theobject beam and reference beam (which must be coherent) when theyinterfere on the surface of the digital imaging device (e.g. CCD). Bysetting up the appropriate optical system, two or more object beams(they can not be coherent) can be brought simultaneously to the CCD. Atthe same time, the corresponding reference beams (one each for eachobject beam) can be brought to the CCD with the ability to adjust theangles between the sets of object and reference beams.

An alternative method is to record multiple SHHs sequentially onto onedigital image. That is, one SHH is imaged onto the CCD, and then asecond is imaged onto the CCD (typically with a different object wave,i.e. imaging a different object surface) with a differentspatial-heterodyne frequency. This is repeated depending on how manySHHs are to be recorded in the single digital image. After the desirednumber of SHHs have been imaged onto the CCD, the digital image is readout and processed.

Referring to FIGS. 16A and 16B two SHHs are shown in a hologram and thentransformed in Fourier space. FIG. 16A is a representation of thespatial-heterodyne fringes of two SHHS. A first SHH 1610 is depictedwith a set of fringes drawn from upper right to lower left. A second SHH1620 is depicted with a set of fringes drawn from upper left to lowerright. FIG. 16B shows the location of these two SHHs in Fourier space.Note that in this implementation, the two sets of spatial-heterodynefringes are near orthogonal, but not at 45 and 135 degrees (closer to 30and 120 degrees). Typically, each SHH has frequency information spreadout along its horizontal and vertical axes. To avoid carrying thisinformation over into the other SHH, the spatial-heterodyne frequenciesare set so that the axes of each SHH in Fourier space do not overlap theother image. Note that each SHH shows up twice in Fourier space, once asa positive image and once as a negative image. The SHHs must bepositioned so that the digital filters 1630 can reject the informationfrom the other SHH and from the main axes in the Fourier image.

Referring to FIG. 17, one possible orientation in Fourier space of threeSHHs acquired in one digital image is shown. Each SHH has beenpositioned, by setting the spatial-heterodyne frequencies, to avoid thecarryover of information from the other SHHs or from the main axes. Itis advantageous to position each SHH in Fourier space so that noise fromthe other SHH(s) does not fall within the digital filter 1710. Again,note that each SHH shows up twice in Fourier space, one positive imageand one negative image.

The invention can include recording multiple-SHHs of different objectsin a single digital image. A major benefit of recording multiple SHHs inone digital image is the increased speed of inspection of an object. TheFourier Transform of the original digital image into frequency space isvery computationally intensive. Being able to transform two SHHs in oneFFT can increase computational throughput by close to 50%. Transformingmore than two SHHs substantially simultaneously confers additionalcomputational throughput efficiency. Another major benefit can beimproved speed of SHH acquisition if multiple SHHs are recorded in onedigital image.

Several methods can be used to image two SHHs onto one digital image. Afirst method for recording multiple SHHs in one digital image is torecord them substantially simultaneously using two separate lasers orone laser split into two separate sets of object and reference beams.Note that when using one laser split into two separate sets of objectand reference beams, the two sets should have path length differencesfrom one another greater than the coherence length of the laser. Thisconstraint simply means that each set of object and reference beams mustbe coherent, but each set must not be coherent with respect to the otherset. Therefore, the two object waves image two different objects,surfaces or views of the same object. The object beams and the referencebeams are then brought together onto the CCD with different spatialfrequencies.

A second method for recording multiple SHHs in one digital image is torecord the two (or more) SHHs sequentially onto one digital image. Inthis method, one SHH is recorded by pulsing or shuttering the laserbeam. Then, the object image can optionally be changed (possibly bymoving the object) and the angle of incidence between the object andreference beams at the CCD is changed (possibly by changing the angle ofthe beamsplitter or the reference beam illumination optics). Uponpulsing or shuttering on the laser beam again, the second SHH isrecorded onto the CCD with a different spatial-frequency. This can berepeated to record more than two SHHs onto one digital image.

A possible variation on this is in off-axis imaging. In off-axisimaging, the object illumination beam is moved from normal incidence tosome angle away from normal incidence. This permits higherspatial-frequency object features to be recorded. These off-axis imagescan be combined with the on-axis image to form an image containing muchhigher frequency information. Using sequential recording of two or moreSHHs in a single digital image, it would be possible to record on-axisand off-axis SHHs in a single digital image. For instance, a first SHHcan be recorded onto the CCD. Then the illumination beam angle ischanged (and the reference beam angle relative to the object beam isalso changed to obtain the desired (e.g., orthogonal) spatial-heterodynefrequency) and a second SHH is recorded onto the CCD. This can berepeated for additionally SHHs, all on one CCD image. The read-out ofthe CCD or digital image can be delayed until all the desired SHHs havebeen recorded onto the CCD. Increasing the complexity of the system toprovide separate incoherent beams for all off-axis and on-axis imagesallows acquisition of the off and on axis images in a single imagecapture.

Referring to FIG. 18, an exemplary apparatus for sequentially recordingmultiple SHHs in a single image is depicted. A shutter 1813 is opticallycoupled to a beamsplitter 1815. The beamsplitter 1815 is opticallycoupled to an imaging lens 1817. The imaging lens 1817 is opticallycoupled to an object 1820. A beamsplitter 1830 is optically coupled tothe object 1820 via the beamsplitter 1815 and the imaging lens 1817.

Still referring to FIG. 18, a shutter 1840 is optically coupled to abeamsplitter 1850. The beamsplitter 1850 is optically coupled to thebeamsplitter 1830. A shutter 1860 is also optically coupled to thebeamsplitter 1850. A CCD camera 1870 is optically coupled to thebeamsplitter 1830.

Still referring to FIG. 18, it should be noted that just one possiblemethod of recording two different object SHHs sequentially in onedigital image by utilizing two separate reference beams is shown and theinvention is not limited to this exemplary apparatus. The operation ofthe apparatus shown in FIG. 18 will now be described. The first SHH isrecorded when shutter 1840 and shutter 1813 are open and shutter 1860 isclosed. An illumination beam 1810 is directed to the object 1820 by thebeamsplitter 1815 and the imaging lens 1817. The reflected light fromthe object 1820 is then collected by the imaging lens 1817 and directedtowards the CCD camera 1870. Simultaneously, a first reference beam 1880passes through the beamsplitter 1850 and is combined with the objectwave by the beamsplitter 1830. The angle of incidence between the objectwave and the reference beam 1880 then sets the spatial-heterodynefrequency. The orientation of the beamsplitter 1830 and/or the angle ofincidence of the first reference beam 1880 on the beam splitter 1830will determine the angle of incidence between the object wave and thereference beam 1880. After this first SHH is recorded on the CCD camera1870 but before the CCD camera 1870 is read out, the object 1820 ismoved and then shutter 1860 and shutter 1813 are opened. Theillumination beam 1810 travels to the object 1820 as before and theobject wave is sent back to the CCD camera 1870, while the shutter 1860allows reference beam 1890 to be incident on the beamsplitter 1850 whichdirects the reference beam 1890 to the beamsplitter 1830 and then to theCCD camera 1870. The beamsplitter 1850 is used to change the angle ofincidence of the reference beam 1890 onto the beamsplitter 1830 so thatthe angle of incidence between the object wave and the reference beam1890 is different from the angle when the first SHH was recorded. Nowthat both SHHs have been recorded onto the CCD camera 1870 withdifferent spatial-heterodyne frequencies, the CCD image is read out andprocessed.

An alternate approach to recording two different object SHHssequentially in one digital image is to use one reference arm but changethe relative angle between the object and reference beams between SHHs.This can be envisioned in FIG. 18 by omitting the reference beam 1890,the shutter 1860 and the beamsplitter 1850. In this configuration, byrealigning the beamsplitter 1830 between each SHH, thespatial-heterodyne frequency of each SHH can be changed. An alternativeway to do this in this configuration is to change the angle of incidenceof reference beam 1880 (or the object beam 1825) onto the beamsplitter1830. By changing this angle of incidence between SHHs, thespatial-heterodyne frequency of each SHH is changed.

Referring to FIG. 19, another exemplary apparatus for acquiring twodifferent object SHHs simultaneously in one digital image utilizing asingle laser source is depicted. A laser 1900 is optically coupled to amirror 1903. The mirror 1903 is optically coupled to a beamsplitter1905. The beamsplitter 1905 is optically coupled to a beamsplitter 1910.The beamsplitter 1910 is optically coupled to a beamsplitter 1915. Thebeamsplitter 1915 is optically coupled to an imaging lens 1920. Theimaging lens 1920 is optically coupled to an object 1925. The object1925 is optically coupled to a beamsplitter 1930 via the imaging lens1920 and beamsplitter 1915. The beamsplitter 1930 is optically coupledto a beamsplitter 1935. The beamsplitter 1935 is optically coupled to aCCD camera 1940.

The beamsplitter 1905 is also optically coupled to a mirror 1945. Themirror 1945 is optically coupled to a beamsplitter 1950. Thebeamsplitter 1950 is optically coupled to a mirror 1952. The mirror 1952is optically coupled to a beamsplitter 1955. The beamsplitter 1955 isoptically coupled to a beamsplitter 1960. The beamsplitter 1960 isoptically coupled to a lens 1965. The lend 1965 is optically coupled toa reference mirror 1970. The reference mirror 1970 is optically coupledto the beamsplitter 1930 via the lens 1965 and the beamsplitter 1960.The beamsplitter 1950 is also optically coupled to a beamsplitter 1980.The beamsplitter 1980 is optically coupled to an imaging lens 1985. Theimaging lens 1985 is optically coupled to an object 1990. The object1990 is optically coupled to the beamsplitter 1935 via the imaging lens1985 and the beamsplitter 1980.

Still referring to FIG. 19, it should be noted that just one possiblemethod of recording two different object SHHs sequentially in onedigital image utilizing a single laser source is shown and the inventionis not limited to this exemplary apparatus. The operation of theapparatus shown in FIG. 19 will now be described. In this apparatus, theoriginal laser beam is split into two parts by beamsplitter 1905 to formBeam #1 and Beam #2. A key point to note here is that the totalpathlength of Beam #1 is sufficiently shorter (or longer) than Beam #2so that at the CCD, Beam #1 and Beam #2 are no longer coherent. Toachieve this, the pathlength difference between Beam #1 and Beam #2 mustbe greater than the coherence length of the laser. Beam #1 is split intoan object beam #1 and a reference beam #1 by beamsplitter 1910. Theobject beam is directed to the imaging lens 1920 and then object 1925 by1915. The reflected object beam #1 then passes back though imaging lens1920 and beamsplitter 1915 towards the beamsplitter 1930. Reference Beam#1 follows an equivalent path, being directed by the beamsplitter 1955and then beamsplitter 1960 through lens 1965 and onto reference mirror1970. The reflected reference beam from mirror 1970 passes back throughlens 1965 and beamsplitter 1960 to beamsplitter 1930. The beamsplitter1930 combines object beam #1 and reference beam #1 with the desiredsmall relative angle between the two. This angle is set by the alignmentof beamsplitter 1930.

Still referring to FIG. 19, beam #2 follows its own equivalent path. Thebeamsplitter 1950 splits beam #2 into object beam #2 and reference beam#2. Reference beam #2 is combined with reference beam #1 by thebeamsplitter 1955 and then follows the same path as reference beam #1.Object beam #2 is directed towards imaging lens 1985 and the object 1990by beamsplitter 1980. After reflecting off object 1990, object beam #2passes back through imaging lens 1985 and beamsplitter 1980. Thebeamsplitter 1935 combines object beam #2 with reference beam #2 (andwith object beam #1 and reference beam #1). It is important to note thatbeamsplitter 1935 is oriented to obtain the desired small relative anglebetween object beam #2 and reference beam #2. Since object beam #1 andreference beam #1 (which have the same overall pathlengths) and objectbeam #2 and reference beam #2 (which also have the same overallpathlengths) travel a distance different by more than the laser'scoherence length, the parts of beam #1 do not interfere with the partsof beam #2; however, since the parts of beam #1 have the same pathlength(within the coherence length) they do interfere, and similarly for theparts of beam #2.

Example 7

The invention can include a method for faster processing of multiplespatially-heterodyned direct to digital holograms. This invention is amethod for increasing the processing speed of multiplespatally-heterodyne holograms. It is based on the realization that aspatially-heterodyned hologram (SHH) occupies only a portion of Fourieror frequency space. The location of the SHH is determined by theorientation and spacing of the heterodyne-fringes in the original image.Therefore, an imaging system can acquire two SHHs (typically ofdifferent objects or locations on the same object), rotate one imagewith respect to the other (so that they occupy different parts ofspatial-frequency space) and add the two images together digitally. Nowone Fourier Transform of the new image will transform both SHH'ssimultaneously instead of requiring two transforms for two images. InFourier space the individual complex wavefronts are located at differentspatial frequencies permitting each to be isolated, filtered, andinverse Fourier transformed to obtain the original complex wavefrontsfrom the object surface.

A limitation of the ORNL patented DDH technology is the significantcomputational-time required to Fourier Transform (FT) the digital imagecontaining the spatially-heterodyned hologram. The computational timerequired for this FT can be up to 50% of the total computational time,thus the ability to process two or more holograms in one FT can resultin a significant savings in computation time.

A key to this exemplary embodiment of the invention is the realizationthat two or more spatially-heterodyned holograms (SHH) can be overlayeddigitally (summed) and then independently isolated in Fourier space byrotating one or more SHHs so that they each have a differentspatial-heterodyne frequencies. The spatial-heterodyne frequency isdetermined by the angle between the object beam and reference beam whenthey interfere on the surface of the digital imaging device (e.g. CCD).If multiple holograms are recorded, each in its own digital image, theSHHs can be rotated and added together. The rotation of the imagescauses the spatial-heterodyne frequencies to be different for eachhologram. Upon adding the holograms together, a single Fourier Transformwill allow the individual holograms to be separated and isolated infrequency space for further processing. This can significantly reducecomputational requirements for analyzing multiple holograms.

In a SHH reconstruction, the first FFT is a real FFT performed on theentire image. Filtering of the carrier signal in the frequency domainand a subsequent complex inverse FFT to acquire the complex wavefrontfollows the FFT. The inverse FFT is typically performed on a subset ofthe image equal to one quadrant or smaller. Therefore, the largestcomputation in the reconstruction stream is the first FFT. As apreferred method of using this example of the invention, two SHHs arecombined by rotating one SHH by 90 degrees and then summing with thesecond SHH. This cuts the number of large FFTs required for a set ofimages in half (one for every two images) at the expense of one imagerotation and one image addition. The rotation does not impact thecomputational requirements since it is a 90 degree rotation and can beperformed in the loading pipline. Therefore, for every two SHHreconstructions, one full real FFT (2N² log₂N multiplies and 3N² log₂Nadds) is eliminated at a cost of one image addition (N² adds). Formemory considerations, this method requires an extra SHH storage areabefore the FFT to hold one image until the second is added. However, ata system level, this is more than compensated for by the reduction inmemory needed to perform and store the results of two separate FFTs.

The invention can include a method for reducing the computationalrequirements for analyzing spatial-heterodyne holograms. After recordingtwo or more spatially-heterodyned holograms (one per digital image), oneof the images can be rotated with respect to the other (one possiblerotation would be to make the spatial-heterodyne fringesquasi-orthogonal between the two images) and then the two images can beadded together. It is important to note that the invention is notlimited to just the rotation of a first image with respect to a secondimage and multiple images can be rotated with respect to a first imageand each other (e.g., rotation of 2, 3, 4 or more images followed byadding all of the images together—each with a different spatialfrequency or rotation angle). Now two or more holograms can be processedin the first Fourier transform and then separated (by application ofdigital filters) in frequency space. This first Fourier Transformrepresents up to 50% of the computational time in analyzingspatial-heterodyne holograms. Therefore, processing two or moreholograms simultaneously in this Fourier Transform can savesignificantly on the computational requirements.

A proof of principle system test of an algorithm implementing thisexemplary embodiment of the invention has been performed using two SHHstaken from a proof-of-principle DDH system. In this system, two SHHswith the same carrier frequency are merged by moving one SHH's carrierfrequency by flipping the SHH along the x axis and then summing the twoimages. FIGS. 20A-20C show a flipped first SHH 2010, a second SHH 2020,and a summed SHH 2030. The zoomed in subimages 2015, 2025, 2035 show theindividual fringe patterns 2015, 2025 in each of the first two imagesand the cross hatch pattern 2035 made by both fringe patterns in thesummed image. It can be appreciated that the flipping yield individualfringe patterns that are substantially orthogonal to one another.

FIGS. 21A-21C show the frequency space representation of the flipped SHH2110, the other SHH 2120 and the summed SHH 2130. The region used toreconstruct a complex wave from the flipped SHH 2115 is circled.Similarly, the region used to reconstruct a complex wave from thenonflipped SHH 2125 is also circled. It can be appreciated that the tworegions 2115, 2125 are well isolated from one another in the summed SHH2130. The only overlap are tails in the X and Y direction. A preferredembodiment of this example of the invention can shift the carrier forthe SHHs off of the 45 degree line and employ rotation. As a result,these tails will not overlap, thereby reducing artifacts caused bysumming the two images.

FIGS. 22A-22D show magnitude and phase images of the two SHHsreconstructed from a summed SHH. FIG. 22A shows the magnitude of theflipped first SHH. FIG. 22B depicts the magnitude of the second SHH.FIG. 22C shows the phase of the flipped first SHH. FIG. 22D shows thephase of the second SHH. In this same experiment, the two SHHs werereconstructed individually (not shown in FIGS. 22A-D) and theirmagnitudes subtracted from the magnitude results of the summedreconstruction (shown in FIGS. 22A and 22B). This subtraction revealednoise levels from the summed reconstruction on the order of 5%. Byselection of the carrier location such that the two images see nooverlap in frequency space, this noise value can be decreasedsignificantly.

An alternative embodiment of the invention can rotate the pixilateddetection device (e.g., CCD camera) between sequential acquisition(recordation) of a plurality (e.g., two) of spatially-heterodynedholograms. The pixilated detection can be rotatable about an axis thatis substantially normal to a focal plane of the pixelated detectiondevice. The degree of rotational freedom thus required by the detectiondevice can be provided by mechanical indexing and/or stepping on an axisin conjunction with an elongated electrical harness (e.g., slack ribboncable), if the magnitude of rotation can be constrained within a limitedarc (preferably less than 180°) or a series of concentric contact tracksor a transmitter-receiver link (radio or optical), if the magnitude ofrotation needs to be unencumbered.

Practical Applications of the Invention

A practical application of the invention that has value within thetechnological arts is high resolution metrology for manufacturing,surface inspection of manufactured parts, 3-D imaging of large objects,a 3-D microscope, and all uses discussed in U.S. Pat. No. 6,078,392issued Jun. 20, 2000, entitled Direct-To-Digital Holography, HolographicInterferometry, and Holovision to Clarence E. Thomas, Larry R. Baylor,Gregory R. Hanson, David A. Rasmussen, Edgar Voelkl, James Castracane,Michele Sumkulet and Lawrence Clow; and U.S. patent application Ser. No.09/477,267 filed Jan. 4, 2000 (published PCT/US00/34982), entitledImprovements to Acquisition and Replay Systems for Direct-to-DigitalHolography and Holovision by Clarence E. Thomas and Gregory R. Hanson.Due to the current use of direct to digital holograhy in thesemiconductor Industry, the invention will be appreciated as havingsignificant application to parts of this market.

The invention is useful for micro-electro-mechanical system (MEMS)inspection. A key feature of the invention in the context of thisapplication is the greatly simplified optical path, specifically thesimplified reference beam optics. The invention can include the use ofpulsed laser beams and synchronizing their pulses to the movement of anobject to freeze the motion.

Traditional holography is based on analog recording of the hologram onfilms or glass plates, because digital recording devices such as chargecoupled devices (CCD) generally lack the resolution to preserve thephase information. The need to process the analog images off-line beforerecorded data can be recovered and digitized for detailed analysis hasprevented the use of holography as an on-line, real-time inspectiontechnique. The DDH technique overcomes this limitation by using a verysmall angle between the object beam and the reference beam, amagnification of the object with respect to the image plane of thecamera, and advances in pixel density of digital recording devices, tomake it possible to digitally record the spatially-heterodynedhologram(s) directly. The resolution of the technique is dependent onthe wavelength of the probing coherent laser light. A version based on adeep-UV laser is presently being developed to achieve real-timeprocessing with 39 nm resolution and 10:1 aspect ratio, using a pulsedlaser, a high density fast CCD, and FPGA-based signal processing toinspect 300 mm wafers at the rate of several wafers per hour. The DDHtechnique, represents a significant advance in rapid, high-resolutiontopographic mapping of static features.

By using pulsed illumination, it is possible to track the motion of MEMSelements. However, because the technique depends on measuring the phaseshift of the probing coherent light source to deduce depth information,it is unable to resolve depths that are multiples of the half-wavelength(λ/2) of the light source. The range of measurements can be extended byusing a very long wavelength, at a cost of resolution. One well-knownapproach to extend the range while retaining the resolution capabilityis to use two wavelengths in close proximity of each other⁽³⁾. In thisapproach, phase information with high resolution is obtainedindependently at two separate wavelengths. These two sets of phase dataare then subtracted to transform the phase data to a scale wavelengthequal to the beat wavelength λ_(b)=(λ₁λ₂)/(λ₁−λ₂) Thus the range can bededuced from the phase of the effective wavelength that is much longerthan either of the two probing wavelengths.

This approach to two-wavelength measurements can be implemented with DDHby sequentially (separate digital images) recording phase images at twodifferent wavelengths, and then obtaining their difference. However,this sequential technique suffers from several limitations. First, noisein each individual image will be uncorrelated. The phase-image noiseresults in height errors proportional to the laser wavelength. When thedifference between the two images is taken, the noise will be carriedinto the difference-phase image, but now it will be proportional to thebeat wavelength λ_(b). Thus the image quality and accuracy will beseverely degraded. Second, any motion in the object between theacquisition of each image will result in pixel-to-pixel differencesbetween the images. When the two phase images are subtracted, new errorswill be introduced due to the pixel-to-pixel changes. Finally, acquiringeach phase image sequentially increases the imaging time and limits thereal-time ability of a potential system.

Since the invention can include obtaining the two phase-imagessubstantially simultaneously using the same optics and digital camera,high-resolution differential-phase images with a scale-length of thebeat wavelength can be generated. Image noise will be reduced becausecommon-mode noise, vibrations etc. will be correlated and cancel outwhen the difference image is obtained. If the two phase-images areobtained substantially simultaneously in the same optics system with onedigital camera, there is always exact pixel-to-pixel alignment andcorrelation. Finally, high-resolution topography is still achievablebecause the phase information for each individual wavelength isrecorded.

The invention can include a method for inspection of MEMS devices usinga Spatial-heterodyne Differential Digital Holography (SDDH) technique toperform pulsed, two-wavelength differential-phase imaging in a singledigital image. As previously noted, because the inventors use theinterference of an object and a reference beam to spatially-heterodynethe object image at a particular spatial frequency, a second heterodynedimage at a different spatial frequency can be generated by introducing asecond laser beam at a slightly different wavelength into the opticssystem. The second laser can be oriented with the necessary angulardifferences to produce quasi-orthogonal, preferably substantiallyorthogonal fringes so that the two images (of the same object area) canbe separated and processed independently even though they are acquiredin a single digital image. The two different wavelength lasers shouldhave substantially no coherence between them to acquire both heterodynedimages substantially simultaneously. A possible arrangement for such atwo-wavelength system is shown in FIG. 1. With this system, bydetermining a difference between (e.g., subtracting) the two phaseimages, it is possible to measure surfaces with topographical (height)variations significantly greater than the imaging laser wavelengths in asingle digital image. These topographical features can include both stepheight changes (cliffs) and continuously sloped surfaces (spheres,wedges etc).

As shown in FIG. 1, this system can utilize a system of two diode-pumpedcrystal lasers to generate substantially simultaneously, but in separatebeam paths, both a tunable wavelength laser pulse and a fixed wavelengthlaser pulse. A fiber optic delivery system can be used to transport thelaser pulses to the necessary location in the interferometer system.Fiber beam splitters can be used to split each laser beam into objectand reference beams. Acousto-optic modulators (AOMs) can be located inthe beam path(s) to allow shuttering and amplitude control of the laserbeams. To obtain the necessary optical mode and polarization, spatialfilters and polarizers can be located at the end of each fiber. From thespatial-filters, the object laser beams enter the free-space opticalsystem where a set of lenses and beamsplitters guide the beams to theobject under inspection and then to the CCD. The reference beams arebrought to the CCD in a similar fashion and combined with the objectbeams to form two quasi-orthogonal holograms in a single image. As canbe seen in FIG. 1, the optical layout is relatively simple and throughthe use of optical fibers, the system can be quite compact.

To implement this system, a fixed wavelength (say at 532 nm) can be usedfor all measurements. The second laser with tunable wavelength (or aselection of lasers at different wavelengths) can be used as the secondwavelength for making two-wavelength measurements. A tunable wavelengthoutput from 500 nm to 531 nm will provide a range of beat wavelengthsfrom approximately 8 μm to 280 μm, respectively, which can be utilizedto accurately measure height displacements to well over 100 μm. Byincorporating several microscope objectives, the field of view can bevaried to acquire high-resolution (better than 1 μm in-plane and 10 nmout-of-plane) and low-resolution (4 μm in-plane and 10 nm out-of-plane)images. This system can measure large displacements both in-plane andout-of-plane for multiple movable elements in a MEMS devicesubstantially simultaneously. By utilizing a 5 ns laser pulse, veryhigh-speed movements can be captured by the imaging system to freeze themotion of moving parts and monitor their dynamic behavior in transientor repetitive motion. Using the stroboscopic effect, repetitive motioncan be captured and replayed in slow motion.

Thus, the invention is useful as a technique for rapid characterizationof the dynamic behavior of movable elements in MEMS devices at the waferlevel. Existing techniques are limited to either wafer level inspectionof static features, which cannot provide information on dynamic responsecharacteristics, or dynamic response of a single element on a die, whichwould not be suitable for use for quality control on a production linethat requires high throughput.

The proper functioning of moving elements in a MEMS device is one oftheir most fundamental performance requirements. There are many factorsthat can contribute toward failure of a MEMS to meet specification.Principal among them are incomplete release and particulatecontaminations during fabrication. Other factors include dimensionalvariations, stringers (extraneous material), undue residual stress, andstiction (bonding by Van der Waals force). These factors can contributeto deviations from design values such as limited excursion range,reduced frequency response, changes in natural and resonant frequencies,power and excitation voltage requirements, etc. or, at worst, resultingin the device being completely non-functional. Therefore, it isimperative that the performance of each device be fully validated. ForMEMS to meet their promise of being able to be mass-produced with highreliability at low cost, such validation needs be performed at the waferlevel with high throughputs.

Although the fabrication of MEMS has benefited significantly fromtechnologies developed for the microelectronics industry in thefabrication of integrated circuits (IC), this is not the case forcharacterization and inspection. This is because there are significantdifferences in their functionality and physical parameters. A comparisonof the key physical parameters and characterization requirements areshown in Table I.

TABLE I Comparison of typical physical parameters of IC's versus MEMSDevice Parameters IC's MEMS Film Thickness (μm) <1 2-6 CriticalDimensions (μm) 0.13 to 0.35 1 Aspect Ratio Generally less than 2:1 Canbe 10:1 or even except for vias greater Topography (μm) <1  4-10 DeviceSize (μm) 1 100 Resolution (μm) ~0.04 <0.10 Range (μm) 1 10's to 100'sMechanical Frequency 0 100's to 1000's Response (kHz)

The challenges for testing MEMS devices can be appreciated by referenceto Table I. Whereas the feature sizes of MEMS devices can be greaterthan that for IC's, the resolution requirements are essentially thesame, while the aspect ratio and the testing range (depth of field foroptical technique) is much greater. In addition, some of the MEMSdevices have moving elements that operate at very high frequencies.Further, because the mass of the moving elements are very small, theirdynamic response is strongly affected by small dimensional and materialvariations, as well as air viscosity and temperature effects. Therefore,characterization and testing need to be carried out in a vacuum capablesystem in which the testing environment can be controlled. From theabove considerations, the basic requirements for testing MEMS devicesduring the fabrication process are: measurement resolution of 10's ofnm; measurement range of 100's of μm; field of view of 10's to 100's ofmm²; depth of field of 10's to 100's of μm; ability to track motion athigh frequencies; high throughput with characterization results providedin real-time; and provide vacuum capable controlled environment. Theinvention is useful for simultaneously meeting all, of theserequirements.

ADVANTAGES OF THE INVENTION

The advantages of the two-wavelength differential spatially-heterodyneddirect to digital holography are twofold. First this technique allowsobjects with depth variation many times greater than the probing beamwavelength to be imaged without losing track of the 2π phase changes. Insingle wavelength spatially-heterodyned direct to digital holography, itis required that each hologram image have at least 2 CCD pixels per 2πof phase shift (2π of phase shift is generated for every λ/2 of heightchange) due to object height changes; less than this and integral valuesof 2π are lost. With the two-wavelength differential technique, therequirement is now that we have at least 2 CCD pixels per 2λ of phaseshift in the differential-phase image, where each 2π is now a result ofheight changes equal to one half the beat wavelength. The two probingbeam wavelengths, λ₁ and λ₂, can be chosen so that the beat wavelengthis many times larger than either λ₁ or λ₂. The additional benefit ofobtaining the two spatially-heterodyned direct to digital hologramssubstantially simultaneously is that noise in the phase (and amplitude)images resulting from back reflections, scattering, vibrations etc. willbe common to both images and so will be reduced when the difference ofthe two individual images is taken.

The terms a or an, as used herein, are defined as one or more than one.The term plurality, as used herein, is defined as two or more than two.The term another, as used herein, is defined as at least a second ormore. The terms comprising (comprises), including (includes) and/orhaving (has), as used herein, are defined as open language (i.e.,requiring what is thereafter recited, but open for the inclusion ofunspecified procedure(s), structure(s) and/or ingredient(s) even inmajor amounts. The phrases consisting of and/or composed of close therecited method, apparatus or composition to the inclusion of procedures,structure(s) and/or ingredient(s) other than those recited except forancillaries, adjuncts and/or impurities ordinarily associated therewith.The recital of “essentially” along with “consisting of” or “composed of”renders the recited method, apparatus and/or composition open only forthe inclusion of unspecified procedure(s), structure(s) and/oringredient(s) which do not materially affect the basic novelcharacteristics of the composition. The term coupled, as used herein, isdefined as connected, although not necessarily directly, and notnecessarily mechanically. The term approximately, as used herein, isdefined as at least close to a given value (e.g., preferably within 10%of, more preferably within 1% of, and most preferably within 0.1% of).The term substantially, as used herein, is defined as largely but notnecessarily wholly that which is specified. The term generally, as usedherein, is defined as at least approaching a given state. The termdeploying, as used herein, is defined as designing, building, shipping,installing and/or operating. The term means, as used herein, is definedas hardware, firmware and/or software for achieving a result. The termprogram or phrase computer program, as used herein, is defined as asequence of instructions designed for execution on a computer system. Aprogram, or computer program, may include a subroutine, a function, aprocedure, an object method, an object implementation, an executableapplication, an applet, a servlet, a source code, an object code, ashared library/dynamic load library and/or other sequence ofinstructions designed for execution on a computer or computer system.

All the disclosed embodiments of the invention disclosed herein can bemade and used without undue experimentation in light of the disclosure.The invention is not limited by theoretical statements recited herein.Although the best mode of carrying out the invention contemplated by theinventor(s) is disclosed, practice of the invention is not limitedthereto. Accordingly, it will be appreciated by those skilled in the artthat the invention may be practiced otherwise than as specificallydescribed herein.

It will be manifest that various substitutions, modifications, additionsand/or rearrangements of the features of the invention may be madewithout deviating from the spirit and/or scope of the underlyinginventive concept. It is deemed that the spirit and/or scope of theunderlying inventive concept as defined by the appended claims and theirequivalents cover all such substitutions, modifications, additionsand/or rearrangements.

All the disclosed elements and features of each disclosed embodiment canbe combined with, or substituted for, the disclosed elements andfeatures of every other disclosed embodiment except where such elementsor features are mutually exclusive. Variation may be made in the stepsor in the sequence of steps composing methods described herein.

Although the holographic apparatus described herein can be a separatemodule, it will be manifest that the holographic apparatus may beintegrated into the system with which it is (they are) associated. Theindividual components need not be combined in the disclosedconfigurations, but could be combined in virtually all configurations.

The appended claims are not to be interpreted as includingmeans-plus-function limitations, unless such a limitation is explicitlyrecited in a given claim using the phrase(s) “means for” and/or “stepfor.” Subgeneric embodiments of the invention are delineated by theappended independent claims and their equivalents. Specific embodimentsof the invention are differentiated by the appended dependent claims andtheir equivalents.

REFERENCES

-   1. U.S. Pat. No. 6,078,392 issued Jun. 20, 2000, entitled    Direct-To-Digital Holography, Holographic Interferometry, and    Holovision to Clarence E. Thomas, Larry R. Baylor, Gregory R.    Hanson, David A. Rasmussen, Edgar Voelkl, James Castracane, Michele    Sumkulet and Lawrence Clow.-   2. U.S. Ser. No. 09/477,267 filed Jan. 4, 2000 (published    PCT/US00/34982), entitled Improvements to Acquisition and Replay    Systems for Direct-to-Digital Holography and Holovision by    Clarence E. Thomas and Gregory R. Hanson.-   3. Wagner et al., “Direct Shape Measurement By Digital Wavefront    Reconstruction and Multi-Wavelength Contouring,” Opt. Eng., 39 (1),    January 2000, pages 79-85.-   4. E. Voelkl, “High Resolution Electron Holography,” Dissertation,    Eberhard-Karls-Universitat, Tubingen, Germany, 1991.

1. A method of obtaining multiple spatially-heterodyned holograms,comprising: digitally recording, at a first reference beam-object beamangle, a first spatially-heterodyned hologram including spatialheterodyne fringes for Fourier analysis; digitally recording, at asecond reference beam-object beam angle, a second spatially-heterodynedhologram including spatial heterodyne fringes for Fourier analysis;Fourier analyzing the recorded first spatially-heterodyned hologram byshifting a first original origin of the recorded firstspatially-heterodyned hologram to sit on top of a firstspatial-heterodyne carrier frequency defined by the first referencebeam-object beam angle; Fourier analyzing the recorded secondspatially-heterodyned hologram by shifting a second original origin ofthe recorded second spatially-heterodyned hologram to sit on top of asecond spatial-heterodyne carrier frequency defined by tile secondreference beam-object beam angle; applying a first digital filter to cutoff signals around the first original origin and define a first result;performing a first inverse Fourier transform on the first result;applying a second digital filter to cut off signals around the secondoriginal origin and define a second result; and performing a secondinverse Fourier transform on the second result, wherein the firstreference beam-object beam angle is not equal to the second referencebeam-object beam angle and a single digital image includes both thefirst spatially-heterodyned hologram and the secondspatlally-heterodyned hologram.
 2. The method of claim 1, wherein thespatial heterodyne fringes of the first spatially-heterodyned hologramare substantially orthogonal with respect to the spatial heterodynefringes of the second spatlally-heterodyned hologram.
 3. The method ofclaim 1, wherein a single pixilated detection device is used todigitally record both the first spatially-heterodyned hologram and tilesecond spatlally-heterodyned hologram.
 4. The method of claim 3, whereinthe single digital image is generated by the single pixilated detectiondevice.
 5. The method of claim 1, wherein digitally recording the firstspatially-heterodyried hologram is performed substantiallysimultaneously with digitally recording the second spatially-heterodynedhologram.
 6. The method of claim 5, wherein a first reference beam and afirst object beam that define the first reference beam-object beam angleare not coherent with respect to a second reference beam and a secondobject beam that define the second reference beam-object beam angle. 7.The method of claim 1, wherein digitally recording the firstspatially-heterodyned hologram is performed before digitally recordingthe second spatially-heterodyned hologram.
 8. The method of claim 7,further comprising changing a path of a reference beam after digitallyrecording the first spatially-heterodyned hologram and before digitallyrecording the second spatially-heterodyned hologram.
 9. The method ofclaim 7, further comprising moving a sample that is characterized byboth the first spatially-heterodyned hologram and the secondspatially-heterodyned hologram after digitally recording the firstspatially-heterodyned hologram and before digitally recording the secondspatially-heterodyned hologram.
 10. The method of claim 1, wherein thefirst spatially-heterodyned hologram characterizes a first sample andthe second spatlally-heterodyned hologram characterizes a second sample.